As stated, forgotten most of the topic but anyways, hope this helps.
A vaccine is basically a pathogen in a liquid that is fed to the bloodstream. This pathogen (the bacteria itself) is either weakened, or tamed, or it is just a part of it. This almost tricks the immune system and white blood cells such as b-cells and helper t-cells come along to fight the virus. When they are fighting it, the helper t-cells almost record the movement and description of the virus (not literally tho). The immune system fights this off easily and later if the same virus comes along (only this time it will be stronger), the helper t-cells will already have the data about the pathogen and the immune system will easily kill it off.
There may be some parts I have missed out (like the terms) but this basically summarizes the main part. Hope this helps :D.