Double consonants are two of the same letters together, such as in the word 'letter' (t is seen twice). Consonants are letters of the alphabet that are not vowels (a, e, i, o, u). As always in English, it's not so straightforward.
Let's take the word cut. That's simple enough, isn't it? But when we add er, do we need to add an extra t or not? In this case we do. Cut, cutter, cutting. If we left it with just one t, it would be cuter which means more cute.
Some words take an extra consonant, and some don't. As always, it's a case of memorising them so keep on practising until you feel confident about spelling. Try this 11-plus quiz for a start and if you don't get full marks, try it again until you do.