Elision is when a sound at the end of one word joins with the sound at the beginning of the next word. This happens a lot in French because the language has a lot of words that end in vowels, and it can be hard to say them all separately without pausing a lot.
For example, imagine someone saying "le homme." It can be hard to say both "le" and "homme" quickly, without a pause or break in between. So, in French, the final "e" in "le" is dropped, and you just say "l'homme" instead.
Another example is "Je aime." It's hard to say "Je" and "aime" without a little break between them. So, the "e" in "Je" is dropped, and you say "J'aime" instead.
Elision can happen with other sounds too, not just "e". It's a way of making French words easier to say and sound smoother.