Philately is a fancy way to say "stamp collecting." If you want to get involved in philately, you can start by saving the stamps from your pen pal's letters.
Philately comes from the French philatélie, which was coined by a 19th-century stamp collector using the Greek phil-, "loving," and atelēs, "free of taxes." This last part explains how a postage stamp works, exempting the recipient from paying taxes on the letter or package they receive. Your interest in philately might be casual, saving stamps from birthday cards — or more serious, collecting and trading valuable or historically interesting stamps.