This term was coined by Wizards of the Coast when they created Magic: the Gathering, the first collectible card game. Magic cards were essentially trading cards, and the concept of the game was always that you would buy a small pack of cards, similar to a foil-wrapped package of baseball cards, for a quick fix of new powers and game options. (In fact, the actual boxed starter pack of 60 cards may have been an afterthought; I'll have to check on that.) Wizards decided on a package of 15 cards, one rare, three uncommon, and eleven common. They called these "booster packs" (boosters for short), named for the sometimes-questionable idea that they were optional. Wizards eventually genericised this term out to their other Deckmaster games, and eventually the term became standard in the then-exploding CCG market.
Some games sold boosters with as few as 8 cards per pack; none went over 15 that I remember. (Today, Wizards has standardized on eleven cards per pack.) Some games had only one level of rarity, some had four or even five. Some games were sold only as boosters, and some non-collectible games created completely static, non-random sets of 15 cards and sold them in a booster-like format (Nuclear War was the first to do this).
Today, the term "booster pack" doesn't just mean a foil-wrapped package of cards - there are slender, boxed boosters for collectible miniatures games, and wide paper-enveloped ones for collectible disk games, and Lord only knows what else. Any game with a random, collectible element, and many games with non-random but optional components, might use this term.