The level up mechanic and leveler creatures were introduced just over a year ago when Rise of the Eldrazi was released. One of the first things to notice about the cards is that there are multiple smaller boxes in the text box of these cards. See Caravan Escort as an example. Each of these smaller sections in these text boxes represent a different set of characteristics that this creature can have.
All of these cards also have the level up ability. This activated ability allows you to pay the level up cost to put a level counter on the creature. The cost to activate these abilities varies and the level up ability can only be played when you can normally play a sorcery. When a creature gains the appropriate number of level up counters, it ‘levels up’ its power and toughness change and it may gain abilities. For example, when Hada Spy Patrol has one or two level counters on it, it becomes a 2/2 creature and it cannot be blocked. When it gains a third level counter it becomes a 3/3, cannot be blocked and gains shroud.
When a creature ‘levels up’ it gains the text included in its new mini-text box as well as the power and toughness that is listed there. When a creature moves from one level to another it loses all text that was in its previous leveled text box.
One final thing to mention is that when a level up creature card is in any zone other than the battlefield, its characteristics are treated as if it did not have any level counters on it.