There is, of course, no direct and tangible benefit for voting. A young person who votes does not personally receive any money or anything like that. Therefore, the benefits have to be either A) intangible and/or B) indirect.
An intangible benefit is the feeling of having done your duty. Young people who vote might feel as if they have done something to help their country. This might make them feel better and more responsible.
An indirect benefit might be that politicians would pay more attention to the needs of the young. Right now, the old vote in much greater numbers than the young so the needs of the elderly are often put ahead of the needs of the young. If more young people voted, this might change because politicians would know that they had to do things to satisfy young voters as well as older voters.
There are millions of young people which makes them an important voting block. Although the young have historically had poor turnout at elections, this apathy could be rectified when they see what a difference their voices made. Instead of complaining about their government, young people need to see that their votes can actually make a difference in who runs their local and national government. If more young people became involved by voting, their age group could actually make a difference in the direction their country goes.