When you level up normally, some of your stats increase, you can equip weapons of that level now, and you get a skill point.
In the OP levels, it’s the same, except you don’t get a skill point (you still go up a level, level-related things still go up, and all that, just no point).
Further, once an OP level is unlocked, you can (at the start of any game) freely choose which level you want to play at. What’s nice about this is that if you balance your character somewhere in the middle (like you get yourself a set of gear that works for you at maybe OP5), if you want an easy time, choose to play at OP0. Your OP5-balanced gear will be that much stronger than those OP0 enemies. Also, if you think OP10 was too easy, try hitting it with OP5 gear. It gives you a wide range of available difficulty levels every time you start. You can make the game easier than Normal mode or legitimately impossible depending on how you work this system, but everyone’s sweet spot is generally somewhere in the middle.
I chose OP3 for my balance level because I wanted more upper range for some of the gear (OP10 shields at OP3, for example, aren’t tissue papers at this high level, for example, and I love Bandit BlASSters, but they’re soft AF unless I’m using one seven levels higher than the local enemies), but you see what I’m getting at.
Just to avoid any confusion, unlocking a new OP level does not increase your stats like health for example. Basically, when playing on an OP level, the world around you levels up by up to ten levels while your character progression is stuck at level 80 (assuming you got the Lilith dlc).
Like @Jefe said, the Lilith dlc is highly recommended if you want to play on OP levels. You get more skill points and some of the best loot in the game, including gear specifically designed for The Raid on Digistruct Peak. And it’s one of the better BL2 dlcs in general.
However, balancing is severely broken on higher OP levels in countless areas. Like @Adabiviak mentioned, a lot of players unlock OP10 and go back down to lower OP levels with their high level gear to reduce the balancing issues. Or you’re one of the people who like to suffer and always play on OP10