Kitten is a plot gift that gives 
(+15) (subject to diminishing returns), specific to Anders.
When Anders has a high enough approval rating he will tell you of a kitten he used to own, you can gift him the kitten you found for more approval (choose the first line "He can stay at the keep, then." - it will net you an additional (+2) approval over the kitten itself, for a total of +13-17). After doing so the kitten will become a usable item in your inventory, Ser Pounce-a-lot.
You can 'use' the item as the Warden or any companion - not just Anders - and he will 'talk' to the kitten, which will meow a response.
Also, you can use him in battle as an item, and he will fully restore everyone's health, even reviving fallen party members.
Location
After regaining Vigil's Keep from the initial darkspawn assault there is a kitten located outside the keep in the courtyard. You can interact with the kitten and choose to pick it up and keep it, if you do so it is added to your inventory as gift.
Trivia
- Amusingly, the program used for lip-syncing means that Anders' mouth will actually move with the kitten's meow.