At its most basic level a home theater computer is simply a computer which is attached to a home theater. It could be big or small, powerful or weak. However, much as a a pencil would make a poor excuse for an eating utensil, some PCs make poor excuses for HTPCs. There is actually a very specific range of attributes which transform an every day PC into a HTPC.
One is size. All computers are trending towards smaller form factors, but for HTPCs, size is particularly important. Home theaters are computers which sit alongside Blu-Ray players and receivers. Compared to the traditional PC tower these are small devices, and the HTPC cases which are normally considered good HTPC cases are much smaller than the traditional ATX tower.
Another attribute which sets a HTPC apart from most office PCs is the absolute need for a video card. Displaying high resolution video is an intensive task which not every computer can easily complete. A good HTPC will need to have a modern video card which is small, quiet, and powerful.
The final and perhaps most important attribute is the control scheme. Normal PCs are controlled by a keyboard and mouse, but such devices are obviously too awkward for use on a couch. HTPCs are instead mostly controlled with remotes similar to those found with a television, although the best HTPC remotes are usually more advanced products like the Logitech Harmony series of Windows-compatible remotes.