The Act empowers the U.S. president to call into service the U.S. Armed Forces and the National Guard:

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).