To “suspend habeas corpus” means the government is temporarily allowed to hold people in custody without letting them quickly go to a judge to challenge whether that detention is lawful.

Put simply:
Normally, if you’re arrested, you (or your lawyer) can file a habeas corpus petition and force the government to “show the body” and explain to a court why you’re being held.

When habeas corpus is suspended, that safeguard is weakened or removed for a time, so people can be detained longer without that immediate judicial check.

In the U.S. Constitution, the Suspension Clause says this can only happen in very rare, extreme situations: “Cases of Rebellion or Invasion” when public safety requires it. Historically, that’s why it’s been invoked around wars or armed uprisings, such as during the Civil War, to allow broader detention powers than would normally be constitutional.