The National Hunt
National Hunt racing usually involves jumping over some kind of obstacles, do it is often referred to as Jumps racing. The races cover longer distances than the Flat, and the winter conditions are often difficult. Tactical racing is the order of the day, rather than going flat out for speed, so races make a fascinating study for those with eyes to see.
A Steeple Chase (or just Chase) originates in cross-country racing over hedges and ditches towards the church steeple, and typically involves water jumps and larger and stiffer fences.
A Hurdle involves smaller fences which are flexible and can be ridden through rather than over, though this is not good practice!
There is an exception to the Jumps rule, naturally. A Bumper is a National Hunt flat race, over longer distances than a true flat. These races are for relatively untried horses who have not raced at all over jumps, and there is a restriction on the number of bumbers a horse can run in. These races are probably best watched for indicators of future form, rather than bet on.
A National Hunt meeting will typically have seven races on the card: three chases, three hurdles and a bumper. The top races are all steeplchases: The Gold Cup, at Cheltenham in March, the King George V Chase at Kempton Park on New Years Day, and of course the Grand National, at Aintree near Liverpool, a week or so before Easter.
The Grand National catches the popular imagination, and the Gold Cup draws large numbers of Irish racegoers, but National Hunt racing generally has a lower public profile than the Flat. Top jump jockeys like Tony McCoy do very well for themselves but are less likely to be household names. Generally it's characterful trainers such as Jenny Pitman or Martin Pipe that attract attention.