Bracken is a species of fern.

Ferns native to the UK normally have one of two growth forms - they either grow in neat clumps, or they spread from underground stolons. Bracken is one of the spreading ones (the other spreading ones, like Marsh Fern, are much smaller and less invasive), which is why it's such a nuisance in the garden.

Just to complicate things, some people call all ferns "bracken".