The term "Audio System" is just a very general way to categorize a group of electronics to play sound, usually consisting of a sound source (CD, MP3, etc), an amplifier (receiver, amplifier, or integrated amplifier), and loudspeakers. An audio system is part of a home theater system, which consists of audio and video sources, amplification, and a display (TV).
As far as what your TV needs, I'm afradi that is a bit vague. What components of a home theater system do you have now? The simplest way to go is an all- in-one home theater system that has a DVD player, amplifier, receiver, and all necessary speakers in one package. If you go this route, stick with a good brand and consult someone who knows what they are doing to set it up. If you are looking to upgrade in the future, go with a seperate receiver and speakers. Again, stay with a good brand (Sony, Pioneer, Denon, Yamaha, Onkyo) and talk to someone about what you plan to do.
An audio system isn't specific, but likely just for playing stereo (2 channel) sound only sources.
A Home Theater audio system is more specific, in that it at least has the 5.1 surround speakers and receiver, which accepts the digital audio from your TV, cable box, DVD/Blu-ray player, and/or or game console, and may even have video source selection and conversion.
Budget HT systems (called HTIB, for Home Theater In a Box) are essentially DVD players with a 5.1 speaker system. Better HTIBs may have digital audio in.