Your IP address is like your own little address on the internet. If it's dynamic, that means it may change every day or few days or week or so -- it's just assigned by your ISP as and when.
If it's static, then it'll always be the same.
Dynamic is useful if you are wanting to spam some forums or something: you can be blocked by your IP address, so once it changes you'll no longer be blocked. It also stops someone from continually tracking you: once they have your IP, it will only be for so long.
If you want to run any sort of web server or VPN server or something from your home computer, it'll be a lot easier if you have a static IP however; that way, to connect to it, you can always just use your own personal static IP.