The wai is the Thai greeting and show of respect, indicated by pressing your palms together near your chest and bowing. Why wai? As a foreigner, you will show and receive respect by following this customary greeting, although many Thais will also (somewhat reluctantly) accept a handshake from you.
The wai is a unique, graceful action practiced throughout Thailand. It plays a very important part in showing respect and is central to Thai etiquette. For the most part Thais do not want to touch your sweaty, grubby little hands, so it's a good idea to learn how to wai. The European kiss-on-each-cheek-greeting will certainly alarm a Thai, especially if you are a man doing this to a woman who isn't your wife or girlfriend!
The wai can be very confusing, especially at large gatherings when you feel like you have been waiing, bowing and smiling a hundred times. However, the plus side is, when being wai-ed to by others you do start to feel quite important!