Eukaryote
In eukaryotic cells, there are many things with membranes around them. All of them together are called the endomembrane system. Simple bags, called vesicles or vacuoles, are sometimes made by budding off other membranes, just like how children make bubbles with their toys. Many cells take in food and other things using something called endocytosis. In endocytosis, the membrane closest to the outside bends inwards and then pinches off to make a vesicle. Many other organelles that have membranes probably started off as vesicles.