The difference between bulls and bears in relation to Wall Street and the stock market is pretty simple. Bulls think that the market, a individual stock, or a industry will rise. On the contrary, Bears think the market will fall.
On Wall Street the bulls and bears can be found wherever you go, because almost everyone believe that one way or another a stock is going to rise or fall, and not stay the same. If you feel strongly that the market is going to rise, than you are what is known in stock lingo terms as "bullish". And, if you feel strongly that the market is going to fall, than you are what is known in stock lingo terms as "bearish".
Being optomistic about the market, the bulls are generally good for the overall vibe. The bull to the left is from the show Mad Money where Jim Cramer is the host on CNBC. Basically Jim Cramer yells a lot and bites the heads off his animals, quite entertaining actually!
TheÃ‚Â opposite which can be seen on the right here is the bear. If you are betting on seeing red, than you are betting on the overall bearish sentiment of the market.
One last point to note about bull and bears, a bullish and bearish opinion can be expressed beyond stocks. You can be bullish or bearish with almost anything, including commodoties like crude oil, futures, options, etc.