The Insurrection Act gives the president authority to call on military and National Guard forces to suppress an insurrection if a state requests it, if there is an insurrection that makes it impossible to enforce federal law, or if there is an insurrection or domestic violence that deprives others of their Constitutional rights.
Here is a little background on the Insurrection Act:
The Insurrection Act of 1807 is a United States federal law that empowers the President of the United States to deploy U.S. military and federalized National Guard troops within the United States in particular circumstances, such as to suppress civil disorder, insurrection, or rebellion.
The act provides a "statutory exception" to the Posse Comitatus Act of 1878, which limits the use of military personnel under federal command for law enforcement purposes within the United States.
Before invoking the powers under the Act, 10 U.S.C. § 254 requires the President to first publish a proclamation ordering the insurgents to disperse. As part of the Posse Comitatus Act of 1878, these provisions are now codified as amended.
There are Constitutional exceptions to Posse Comitatus restrictions rooted in the President's own constitutional authority. Defense Department guidelines describe "homeland defense" as a "constitutional exception" to Posse Comitatus restriction, meaning that measures necessary to guarantee National Security from external threats are not subject to the same limitations.
when requested by a state's legislature, or governor if the legislature cannot be convened, to address an insurrection against that state (§ 251),
to address an insurrection, in any state, which makes it impracticable to enforce the law (§ 252), or
to address an insurrection, domestic violence, unlawful combination or conspiracy, in any state, which results in the deprivation of constitutionally secured rights, and where the state is unable, fails, or refuses to protect said rights (§ 253).
The 1807 Act replaced the earlier Calling Forth Act of 1792, which had allowed for federalization of state militias, with similar language that allowed either for federalization of state militias or use of the regular armed forces in the case of rebellion against a state government.
The 1807 Act has been modified twice. In 1861, a new section was added allowing the federal government to use the National Guard and armed forces against the will of the state government in the case of "rebellion against the authority of the government of the United States," in anticipation of continued unrest after the Civil War. In 1871, the Third Enforcement Act revised this section (§ 253) to protect Black Americans from attacks by the Ku Klux Klan. The language added at that time allows the federal government to use the act to enforce the Equal Protection Clause of the Fourteenth Amendment to the United States Constitution.:63–64 This section of the act was invoked during the Reconstruction era, and again during desegregation fights during the Civil Rights Era.
The chief clause of the Insurrection Act, in its original 1807 wording (which has been thoroughly updated since to reflect modern legalese), reads:
An Act authorizing the employment of the land and naval forces of the United States, in cases of insurrections Be it enacted by the Senate and House of Representatives of the United States of America in Congress assembled, That in all cases of insurrection, or obstruction to the laws, either of the United States, or of any individual state or territory, where it is lawful for the President of the United States to call forth the militia for the purpose of suppressing such insurrection, or of causing the laws to be duly executed, it shall be lawful for him to employ, for the same purposes, such part of the land or naval force of the United States, as shall be judged necessary, having first observed all the pre-requisites of the law in that respect.
In 2016, Public Law 114-328 was amended to include Guam and the US Virgin Islands under Ch. 13 jurisdiction. §252: "Use of militia and armed forces to enforce Federal authority" currently reads:
Whenever the President considers that unlawful obstructions, combinations, or assemblages, or rebellion against the authority of the United States, make it impracticable to enforce the laws of the United States in any State by the ordinary course of judicial proceedings, he may call into Federal service such of the militia of any State, and use such of the armed forces, as he considers necessary to enforce those laws or to suppress the rebellion.
The Insurrection Act has been invoked throughout American history. In the 19th century, it was invoked during conflicts with Native Americans. In the late 19th and early 20th centuries, it was invoked during labor conflicts. Later in the 20th century, it was used to enforce federally mandated desegregation, with Presidents Dwight D. Eisenhower and John F. Kennedy invoking the Act in opposition to the affected states' political leaders to enforce court-ordered desegregation. More recently, governors have requested and received support following looting in the aftermath of Hurricane Hugo in 1989 and during the 1992 Los Angeles riots.
In 2006, the George W. Bush administration considered intervening in the state of Louisiana's response to Hurricane Katrina despite the refusal from Louisiana's governor, but this was inconsistent with past precedent, politically difficult, and potentially unconstitutional. 73–75 A provision of the John Warner National Defense Authorization Act for Fiscal Year 2007, added by an unidentified sponsor, amended the Insurrection act to permit military intervention without state consent, in case of an emergency that hindered the enforcement of laws. Bush signed this amendment into law, but some months after it was enacted, all fifty state governors issued a joint statement against it, and the changes were repealed in January 2008.
On June 1, 2020, President Donald Trump warned that he would invoke the Act in response to the George Floyd protests following the killing of George Floyd. In his official statement, Trump urged "every governor to deploy the National Guard in sufficient numbers" to re-establish civil law and order "until the violence has been quelled"
How does it differ from martial law?
The Insurrection Act is a law while "martial law" is a concept that doesn't have a legal definition in the U.S. "It's not enshrined anywhere," said Thaddeus Hoffmeister, a law professor at the University of Dayton.
Generally, martial law means that the military takes over civilian control of the government, whereas the Insurrection Act applies to specific instances of rebellion or refusal to uphold the law and requires a state's National Guard or the U.S. military to intervene.
Martial law is essentially the absence of law. It would apply to situations where the rule of law has broken down so much that law is no longer in place.
Could Trump still invoke the Insurrection Act?
While the law is broad and gives the president discretion in its use, There are certain conditions that would need to be met before a state's National Guard or active duty military were deployed under the act.
If Trump were plotting to invoke the act in some effort to prevent the transition of power to Biden, he'd have to declare it, as part of the provision in the act requiring essentially a public cease and desist order for the insurrectionists.
He couldn't do this surreptitiously. He would have to make a public proclamation and that would expose his objectives and partisan rationale.
Furthermore, it's unlikely that active-duty military would follow through with the order in such a case where there isn't violence or insurrection.
When you invoke the Insurrection Act, it doesn't necessarily mean that everything is going to grind to a halt. It doesn't mean that the inauguration doesn't go forward.
Hopefully this video will give you more of an undersanding.