To run into someone means to meet them unexpectedly, without planning it. You might run into your teacher at the grocery store, or run into a friend from summer camp while on vacation. The phrase suggests surprise: you weren't looking for the person, but suddenly there they are.

The expression comes from the idea of physically bumping into someone, though you don't actually have to collide. When you say “I ran into Maria at the library,” you mean you saw her by chance, not that you literally crashed into her.

You can also run into problems or difficulties. A scientist might run into unexpected challenges during an experiment. A construction crew might run into solid rock while digging. In this sense, the phrase means encountering obstacles you didn't anticipate, things that get in your way or slow you down.

Less commonly, run into can mean physically crashing into something, like when a distracted driver runs into a parked car or a skateboarder runs into a fence.