2.61 understand that vaccination results in the manufacture of memory cells, which enable future antibody production to the pathogen to occur sooner, faster and in greater quantities

If you get infected with an infection (duh) it can take a while for your phagocytes to produce the antibodies needed to lock onto the antigens. This obviously is bad because your condition could severely worsen etc. To avoid this, you can have a vaccination. All a vaccination is is injecting dead (or inactive) pathogens of that particular infection into your body. Although the pathogens are dead, your lymphocytes will still recognise them as foreign objects and will still produce antigens to deal with them. Some of these lymphocytes will remain in the blood as memory cells, so if another pathogen of the same infection (e.g. if you really do catch the disease), the pathogens will recognise that pathogen and will be quickly able to produce antigens to destroy them in great numbers.

NOTE: If you are unsure of what pathogens do, or the difference between pathogens and antigens, have a look here... 2.60