Playing "in time" is a term musicians use to mean playing with the beat. This is a skill that, like most skills, comes easier to some than others, but- again, like most skills- can be improved and mastered with practice.
Musical elements
Music is made up of three basic elements: Melody, rhythm, and harmony.
Melody is, well, the melody. The notes you play.
Rhythm is how long or the notes are.
Harmony is how the notes fit together.
Playing in time is a very important skill for any pianist (or any musician in general) especially if one wishes to play with other musicians. Imagine a rock band in which the keyboard player is playing faster than the drummer, and the guitarist is playing slower than everybody else...this would be a train wreck.
Playing in time is also important for solo performances, as you want your audience to be able to feel the beat of the piece (assuming the piece isn't rubato AKA intentionally not in time)
Rushing
One common mistake that pianists make is rushing. They start at a good tempo and gradually speed up until, by the end of the piece, they're a good 20-30bpm (beats per minute) faster than the starting tempo.
Improving your time is simple: Play with a metronome. Notice I said "simple", not "easy". It takes time to improve your time. If you practice daily with the metronome, your time will gradually get better and better.
Here's an example of a Katie, a student of mine, working on playing in time...our metronome was a pre-recorded rhythm track on a keyboard.
Teachers, take note: Rhythm tracks are a great way to help a student practice playing in time without using the dreaded metronome.