Some of you may not realize what this word means, but in short: it means being fair and understanding the feelings of others. The dictionary defines it thusly.
com·pro·mise (kmpr-mz) n. A settlement of differences in which each side makes concessions.
When we argue with family and friends we may be able to reach a sensible conclusion to the problem by reaching a compromise with them. During your teen years you are full of hormones and you are very liable to fly off your handle at the slightest problem! A lot of arguments can be avoided if you compromise.
I'll give you an example. Say your Mom doesn't like it when you come home, grab a coke from the fridge, dump your dirty sports kit on the kitchen floor and then retire to the sitting room to lounge around in front of the TV for a while rotting your brain. The compromise for this would be to come home, perhaps talk to those parental units about your day, put your dirty sports kit in the washing machine/wash basket and then retire to your bedroom to do half an hour of homework before slumping in front of the television to continue the important rotting of brain cells.
When bargaining with somebody, you can always make sure you get a fair deal by reaching a compromise with them. When bargaining with your parents, before leaving for the party of the year, offer your curfew time. It is a good idea to suggest something extreme first, like 5am. They will say, No! don't come home any later than 10pm! So then you say, how about 12am if I call before I leave so you know I am on the way? And they'll agree with a time around that point.
Getting your way in a relationship can also be about compromising certain aspects. Maybe your significant other is the one who always pays for everything of the both of yours. Compromise to pay the next time. Say you and your honey go and buy pizza. Let them pay for this pizza, but you offer to buy the next. This way, you save a bit of money right then, and later on, the favour is returned to them when you buy the pizza the next time.
When sharing out household chores, parents might land you with all the rotten ones. This is where compromise comes into play again. Do some of the rotten ones, like taking out the garbage, but make sure you have some decent ones, such as walking the dog during the summer, or loading the washing machine when it needs doing, or vacuuming (it's good if you turn on some music while you vacuum).
Many arguments can be brought to a quick end if compromise is remembered. Always compromise and people will think you are mature. Nice thing to remember :)