Really there's two parts to it. The Enchanted Forest is a child-centred woodland walk, with walkways, animals (including pigs and peacocks) and best of all some giant tree swings.
The current house itself was built for Philip Packer in 1662, and his friend John Evelyn helped him design the gardens. Evelyn of course lived in Deptford at Sayes Court, with its own famed gardens.
Some of the features of Evelyn and Packer's garden remain (see detail at London's Lost Garden)
Groombridge Place has featured in a number of films, most notably the 2005 version of Pride and Prejudice (with Keira Knightley) and Peter Greenaway's great 1982 film 'The Draughtman's Contract'
Tip: take a picnic and eat in the fields outside before you pay to go in, there's plenty of space. Obviously you don't have to have kids to go, the gardens are worth a visit. Peaks season it's £10 in for adults, £8.45 for children (prices include admission to Enchanted Forest and formal gardens) so it does work out quite expensive if you are in a big group - though there are some family ticket deals and children under three are free.