Once I got prestige-1 I though that it will increase along with increase of XP-levels. But now i'm level 47 and prestige is still 1, so I start to wander was I correct or not. What does the prestige depend on?
You gain a level of prestige every time you reach the maximum player level. Your level can be seen at the end of each game : it is the gauge filled with the solars gained. Remember that level also enable new upgrades for characters.
When you have reached the level 138 (see this question), a text box will ask you if you want to upgrade your prestige level:
There are 10 prestige levels and when you get a new level of prestige, you loose every upgrades unlocked before (you will have to get them again by playing and gain player level...)