What's part of an hour? A minute, or minutes! This word is the suffix version of 分, so it goes after numbers to say how many minutes, and is used for telling the time too.
This uses a different on'yomi than what you learned with the kanji, so here's a mnemonic to help you remember this reading:
How many minutes of fun (ふん) will you have today? Lots and lots of minutes, I hope!
Depending on the number before 分, its pronunciation can change to ぷん, because of rendaku. We're looking for the original reading ふん here though!
It generally takes about two minutes.
Shall we rest for fifteen minutes?
It's about five minutes on foot from my apartment to a convenience store.