Look up "electrolytic capacitor" on Wikipedia for a better explanation than I could give!
It's not a difficult job, but it does take a bit of practice and you need the right equipment. It mostly just takes time. If you do do it, make sure you use a good, fine, temperature-controlled soldering iron for through-hold capacitors, and use an SMT rework station for the SMT capacitors.
If you've never done soldering before probably best leave it to someone else until you've had a bit of practice. And don't worry too much, your Amigas won't just suddenly blow up now you've read that capacitors can get old.

Just keep an eye out for symptoms (screen interference, long boot-up times, distorted sound, that sort of thing.. anything that just seems "odd" is usually capacitors!)