The Level Number can be seen above your head, after your name, in public rooms.
No one really knows for sure why Levels were bought into the game or exactly how they work. I suspect it was for monetary reasons.
The higher the level number, it seems, the more that player is active in game play and more money is invested in the game by them.
More experienced players can tell you the things that can rise or lower it. Most is trial and error.
I know I have gifted, bought clothes and poses and my levels have remained the same. My spouse has done the same and her level rises.
From this I presume you have to spend a certain amount before the level rises for men and possibly the levels are kinder to girls. Who knows!!
The things that seem to effect the level are :
Amount of friends, lovers, spouses. The more you have, the higher the level. As you lose / delete them, the level lowers.
Sex in private & public also seems to rise the levels.
Spending money in the shop buying items or A$
Buying properties in the public rooms
Rating sex poses
Public likes
Basically, the more you experience the game : spend, gift and play and are an active player, your level will rise.
You also have the opportunity now of buying levels to feed off the need to belong and look more attractive to other players.
Good Luck with that, if that is what you want.
As for me, I enjoy the game the way I want to and levels be damned!