Including
Included, Furnished With, Attached To
suffix
You know that the kanji 付 means attach and words like 付く mean "to be attached." This has the same idea. When you see this attached to another word, for example, you might know that something is attached to something else, or perhaps included with it. For example, if you stay at a hotel room, maybe it is a breakfast付き, i.e. "including breakfast."
The reading comes from the reading of the kanji as well as from words like 付く and 付ける.
三食付き
three meals included
サンプル付き
sample included
おまけ付き
free gift included
このスプーンはケース付きですよ。
These spoons come with a case.
この辺にプール付きのホテルはありますか？
Is there a hotel with a pool around here?
この部屋は冷蔵庫、洗濯機付きです。
This room is furnished with a refrigerator and a washing machine.