Giverny is located in the Eure département (27), about 80 kms away from Paris.
If you happen to go to Giverny, it's probably to visit Claude Monet's house. Beside the house, there's a also a nice flower garden, called "Le Clos Normand", the water garden ("Le Jardin d'Eau") with its green Japanese bridge and the famous nymphéas, and a really well stocked gift shop housed in what used to be Monet's workshop ("Atelier des Nymphéas"). There are two rooms in the house that are really striking: the dining room with its yellow walls and furniture (there's a nice collection of Japanese prints on the walls too) and the kitchen with its blue tiles made in Rouen and its gigantic stove.
Claude Monet married twice. He had 2 kids with his 1st wife, and inherited 6 from his 2nd wife (some say the youngest one might have been his). Claude Monet lived in the Giverny house from 1883 to 1926, that's more than 40 years. One can easily imagine the ambiance at the house with all those kids running around.
For more info, visit the fondation Claude Monet which is in charge of the Monet house in Giverny.