Houdini is strapped into a regulation straight jacket by spectators, but is able to extricate himself while in full view of the audience. As the years went by, Houdini sought to make the straightjacket escape more difficult. He did so on many occasions by escaping while, for example, suspended upside down, plummeting over Niagara Falls, being attacked by a swam of bees, or asleep.
We discuss straightjacket escapes in general elsewhere, but the information on that page does not apply to the great Harry Houdini.
Houdini was a perfect physical specimen and completely in control of his physiology. Not only could he stop his heart and central nervous system at will and dislocate any joint in his body, he could also voluntarily collapse his ribcage and cause his internal organs to line up in alphabetical order (with some exceptions for poor spelling in the intestines).
By leveraging his abilities, Houdini could in fact simply compress his body and squirt out the top of the straight jacket like toothpaste coming out of a tube, often causing his audience to faint, wildly applaud, and/or vomit.