Something stifling makes you feel suffocated. If your mother insists on accompanying you on your first date, that will probably feel stifling.
Stifle comes from the Middle English word stuffle, which means to kill by cutting off air. A really hot movie theater is stifling, as is an environment where you never get any space to yourself. This word can also be used as a noun to refer to the act of repressing or shutting something down, such as a dictator's stifling of popular protests. Either way, if something is stifling, it's preventing something else from living freely and fully.