ELO boosting helps players achieve their goals in a variety of different ways. For some players, unlocking the end of Season Victorious skin is their only goal for the year and these players sometimes need a helping hand to get there. Other players are determined to beat their previous seasons rank or even get into Master tier. Some players just want to beat their friends and will do anything possible to make sure they finish in a higher division. Whatever goal a player has, elo boosting can help them achieve it.
In terms of the benefits from elo boosting, there are actually a lot. The first benefit is that the player doesn't have to spend all day playing games and can actually focus on other things in their life. Some players get so fixed in trying to reach a particular division or achievement, that they often neglect other parts of their life. This is obviously not healthy and can often lead down a dark path as the player is consumed by LoL.
Instead, a booster can help take the burden off you by giving you a helping. This gives you plenty of time to do other stuff in your life while knowing you're still on your way to achieving your in game goals.
Another benefit of elo boosting in League of Legends is that it can save you a lot of time. Imagine you're in Bronze 1 and want to get to at least Gold 5. You could spend months and months trying your hardest to get there, or you could pay a booster to get you there in a few days. Would you rather waste a month of your life? After all, life's too short!