This is a VERY broad and vague question, and would be better answered by doing some research. I'm sure that googling "LCD versus plasma" would turn up many, many articles covering this topic to death and then some. AVSForum is another good site for home theater questions.
Relatively short answer (without getting into how the technogies differ; suffice it to say they are VERY different technologically):
Plasma displays have better contrast ratio and color saturation, and are easier/cheaper to make in extremely large sizes (50-60" and up). As downsides, plasma screens can suffer burn-in and can fade significantly over time (requiring expensive repairs). They can also be *hot*, and use a lot of power (neither is normally a huge issue for a home theater, though).
LCD displays tend to have slightly worse contrast ratio and color saturation, and sometimes (especially in cheaper models) have a 'screen door' effect from the inter-pixel spaces. LCD displays tend to be easier/cheaper to make in smaller sizes. They would, as a whole, tend to hold up better over time, and replacing a fading LCD backlight is far cheaper than recharging a plasma display. They also should not suffer from burn-in (at least not nearly as badly as plasma).
In practice, both are pretty damn good these days, and both are still very expensive when you start talking about big displays.