A carbocation is a positively charged species.  The positive charge is localised on an sp² hybridised carbon atom.  Hence the carbocation itself is planar around this carbon.  The p orbital of the sp² carbon is empty. Typically they are significantly stabilised if the positive charge can be delocalised across the molecule, and thus they form a part of our discussion of resonance.

As already noted, alkyl groups donate electron density, and hence the more of these groups surrounding the sp² carbon, the more stable it will be.

Methyl	<	Primary	<	Secondary	<	Tertiary

This helps us to explain Markownikow's rule in more detail; it is actually just a disguised way of saying the most stable carbocation forms preferentially.

There are other ways to stabilise carbocations, for example, we can use the empty p orbital to spread the charge:

We can extend the concept above further, and spread the charge into a benzene ring in the same manner.

A curious example of an unlikely looking stabilised carbocation is:

This seven membered ring is actually aromatic, which is where it achieves its surprising stability.