Wood carving shares a lot of similarities with stone carving inasmuch as both were used primarily to decorate temples. You can see traditional wood carving used to decorate the pillars and beams used to support the roofs of temples (and lately restaurants as well). However understanding that wood carvings are much easier to transport and have more practical uses in home decorating it should come as no surprise to learn that Westerners have begun to have a strong influence on what is now being produced. Not that that is all bad. Traditionally wood carvers have also had pretty much free reign to experiment and many have become more sculptors than carvers with the best wood carvers turning unusual pieces of wood that most folks would just as soon throw away into masterpieces. However, still the most sought after works are the traditional Ramayana figurines.
There are many varieties of wood used. As a general rule of thumb all things being equal the softer the wood the faster it grows and the easier it is to carve and hence the price is lower. Popular soft woods are merantie, crocodile and hibiscus. Harder woods such as nangka (jackfruit), and kampor are much heavier and can be more intricately carved. Either way a word of caution - The wood is not always thoroughly dry before being carved and if you take it to a climate with less humidity it may crack. So sometimes it's better to take the older carving that's collected its share of dust and polish it up yourself when you get back home.