The last person who worked on your board didn't do a very good job cleaning it up.
It happens often. A lot of people skip that final, crucial step of removing flux.
The brown stuff is rosin flux - somewhat like pine sap It's a component in rosin core solder that helps clean things and helps the solder flow.
Flux should be removed after soldering. Kind of like wiping ones posterior after using the facilities.
How to remove it...
91% or better isopropryl alcohol or naphtha
IPA can be had at most drugstores or department stores. It's more expensive than the 70% stuff, as it's diluted less.
Naphtha is cheaper, but has a stronger odor and may be more flammable.
Take a toothbrush, and some IPA, and scrub.
If it's really stiff and dried out, you can take a dental pick, or something similar, and scrape some of it away before cleaning it.
The way you get the best results - get some kimwipes.
You can buy these at medical supply stores, on eBay, and some office supply stores. I mail order mine, as I couldn't find them locally. Kimwipes are lint free, and are softer than tissues.
I take a brush, and brush the area I'm cleaning with IPA or Naphtha, and then put a kimwipe over it, and brush it some more.
The kimwipe absorbs the flux. Otherwise, you're just rinsing it around the board.
Some really tough areas, you may use 2 or 3 kimwipes - but once you get the process down, the board will be clean and residue free.
Another tip - use *good* solder. Not just whatever crap your local radio shack or hardware store has on the shelf. I use Kester 24-6337-8800 - it's 'no clean', meaning *technically*, the flux doesn't need to be cleaned up, but do it anyways! Any job worth doing is worth doing right! And it's not that expensive, about $18 per 1# roll. Most people will get a lifetime's worth of service out of a single 1# roll. I get mine from Kimco - gokimco.com - but since you're in Canada, you'll probably want to find a Canadian distributor, so it arrives faster and costs less to ship.
I'll be honest - you're gonna be mad at that board by the time you're done. It's gonna be a bit of a pain to get clean - but it'll look so much better when you're done - even though you won't be able to see the back once it's installed!
One more thing...
If you've never done board work before, don't start with this board. It looks like it's still pretty nice. Not doubting your skill, or implying anything - just suggesting you find some old junk electronics to practice on first. Work your way up to it. The clue is looking for something *old* - any recently made electronics won't be similar to that board at all. Practice til you can remove and replace components without lifting traces or burning the board. I do a lot of PCB repair for a number of customers,and more often than not, if someone sends me a board after they tried to fix something, they've made it worse, because they shouldn't have been in there to begin with. A nice unhacked board is easier to diagnose, which means it costs people less in the long run, and it's also much easier to repair without doing damage. The way you fix a damaged PCB is not always cosmetically attractive. Some people care, some do not.
So, ask questions, practice on something that's not important first, and don't be afraid. Just be respectful of what you're trying to repair.
Oh yeah, don't forget to have fun!