Fantasy worlds contain magic, and magic is a strange force that responds to an intelligent will, in accordance with certain rules, to bring about alterations or other manifestations without other more mundane means. Magic is sometimes used to do things that are otherwise impossible (without it), or as an alternative to conventional means.
Describing magic being used is tough if you don't want to use conventions like wands, spells, whatnot; and if you do, it is all too easy to fall into familiar clichés. Terry Pratchett famously invented a color for magic (and a smell, and a taste in the air), giving him a familiar, personal and non-clichéd shortcut each time he used it.
Describing magic is tough. Spend some time thinking about it, and describing it to other people – e.g. your highly critical spouse who doesn't like fantasy.