Gnomes live in gnome-holes underground, where they dig up plant roots and generally cause a mess; their presence is also a dead give-away that a home belongs to a witch or wizard (Sch1). Gnomes are rather dim, so when they realize a de-gnoming is going on, they all come rushing up out of their holes to see what's going on, making them a lot easier to catch (CS3). Crookshanks loved chasing gnomes around the Weasleys' garden and the gnomes seemed just as much to love being chased (GF5).
One December when Fred Weasley was bitten by a gnome while picking carrots in the garden, he grabbed it and put it on top of the Weasley's tree: "Stupefied, painted gold, stuffed into a miniature tutu and with small wings glues to its back, it glowered down at them all, the ugliest angel Harry had ever seen, with a large bald head like a potato and rather hairy feet". Harry, Ron and George were the only other people who knew about this less than savoury origin of the Christmas angel (HBP16).
Xenophilius Lovegood thought the Weasleys had a "glorious infestation" of gnomes. According to him, the scientific classification of the gnome is "Gernumbli gardensi" (DH8). He was extremely excited when Luna was bitten by one when she stopped to say hello to them, as he believed the bite of a garden gnome could bestow special gifts on a human through the Gernumbli magic in the saliva, such as the ability to speak the language of Merpeople (Mermish) or suddenly sing opera. But to the rest of the Wizarding World they are merely a garden pest (FB).
Gnomes seem to have rudimentary speech; they squeal "gerroff me!" when the Weasleys degnome the garden (CS3), and Ron tells Xenophilius Lovegood that their gnomes know "a lot of excellent swear words" probably taught to them by Fred and George (DH8).
The gnome has been popularized through modern culture as the garden gnome. A garden gnome is typically a small human-like creature with a long white beard and a pointy hat that people keep as decorations in their lawns (Wikipedia) - what Ron describes as "fat little Father Christmases with fishing rods" (CS3).