My brother does computer graphic rendering and animation, like for short CG movies, but the computer is getting too slow for it, and he wants to know what parts to upgrade to speed it up; should be boost his GPU, or is that not how that kind of rendering is handled?

It depends on the software, I'd guess. Generally this was always a cpu-task - nowadays I can imagine that they use also GPGPU. But perhaps you need the pro-cards (Fire GL, Quadro) to make GPUs work with the software. Which software does he use? Also, what are his specs? Intel has also introduced acceleration-units on its processors. Also, make sure the program has sufficient ram to work on.

I think hardware rendering would entail that GPU is doing the rendering. Software rendering that it's on the CPU.

I don't know much about this, but I think most programs use hardware rendering while you're working with modeling/animation, and software to produce the final output. Though I guess if it used GPGPU functionality to render that would also benefit from a good graphics card. Pro graphics cards are expensive and not a necessity if your brother is not being paid handsomely for his work. All this info could be outdated, though, so take it with a grain of salt.

Poster above me is right.

Any good software suite though should rely on the GPU for allot of the hard work, that's not to say the CPU isn't important however.
But if you are unsure, let us know the software and the hardware it's running on and we should steer you in the correct direction.

CGI should know all about it ask him lol