Ok this is pretty straightforward, during the day your teeth get caked up with bits of food and debris. The sticky mix of food left overs, and the bacteria that thrive therein, is called PLAQUE. Plaque is EVIL. EVIL. Plaque causes tooth decay (acid produced by the bacteria dissolves the tooth) and gum disease (toxins produced by the bacteria cause inflammation in your gums - that's why they go red and bleedy - eventually your teeth drop out).
So that's why we need to brush to get rid of the plaque.
Manual or electric brush? Who cares as long as you get rid of the plaque. Flossing and little inbetweeny brushes (such as TePes) help but brushing is the big thing. If you don't brush you will get problems, and smelly breath so no one will want to kiss you.
Brushing is particularly important before bed because your mouth dries up when you are sleeping (especially after ten pints of Stella in The White Bear) and the protective effect of saliva is diminished. To put it another way any plaque left on your teeth while you are asleep causes more damage than during the day.
As mentioned above brushing is important as it removes plaque (evil, evil plague) and plaque is the root cause of tooth decay and gum disease.
Gum disease is important because more adults loose teeth through gum disease than decay. As you get older your teeth become more resistant to decay but, generally, more susceptible to gum disease.
Now as a studious teenager you won't have had much gum disease (partly because of all the hyper-salivation teenagers experience, remember saliva protects) but as you get older gum disease can creep up on you and cause irrevecable damage.
Be aware that bleeding gums are (usually) a sign of gum disease. It means you've left a load of plaque on your teeth. Try brushing for a bit longer in the first instance, i.e. try getting rid of more plaque, and see if you can reduce the bleeding.
If in doubt see a dentist and get them to check your gums. Gums are important, they keep your teeth in.