The expressions levelling or to level derive from the concept of level thinking. At the poker tables this means that before you choose an action, you try to think on the level of your opponent in order to figure out what impression the action will give him. You basically think about what he might be thinking.
You can of course continue this and come up with an infinite number of levels - "what does he think that I think that he thinks that I think…" and so on. This is referred to as second level thinking, third level thinking, etc.
There may be some patterns in your game that other players might detect. For example, you might occasionally try to take the pot with a pure bluff on certain boards in certain situations. If you are in such a situation, but fear that your opponent is aware of how you will play and that he might therefore re-bluff, you might also be tempted to bluff again and so on.
This can work out fine, but it could also happen that you are levelling yourself into an action at the table. This would be the case for example if you get too caught up in your level thinking when you try to justify a specific action, while the opponent isn't even giving the situation any further thought because he already has the nuts.