The tattoo chair is an object for The Sims 3: Ambitions. It was supposed to be used to increase the Tattooing skill, which will also come with Ambitions. In the preview shown by gamespot, the tattoo chair is seen as an item which can be bought by Sims to use at home.
There are two types of tattoo chairs. The first is The Ink-in-Comfort 3000 which is used by a Tattoo Artist or other sim to apply tattoos to another sim the old fashioned way and the other is The Digital Tattoo Applicator which is an automated tattoo applying machine.