In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. But what does that have to do with the movie?
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I'd like to invite you to the SciFiStackexchange, that has quite a few questions about this movie – Yasskier Jan 10 at 1:15
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@Yasskier oh, thank you. I'll take a look. – R S Jan 10 at 6:30
It's the name of the spaceship they go to rescue.
The Event Horizon was built with a gravity drive, designed to generate an artificial black hole and use it to bridge two points in space, thereby reducing travel time over large distances.
To enter a black hole, one passes the event horizon.