Cellophane is a good analogy. It is a semi-permeable membrane which is permeable to water and small molecules, but not to large molecules, and can be used to demonstrate the principal of osmosis. Cellophane is made out of plant fibers called cellulose but living membranes are made out of layers of fat cells.
Many textbooks will compare a cell membrane to the fluid mosaic model, which means that the parts of the membrane (phospholipids, cholesterol, proteins etc.) are not stuck in one place; they move around and can pass by one another while still keeping the integrity of the membrane. That is mainly for the structure, but structure always lends to function.
You could use lots of analogies. Cell membranes keep the traffic of things going on in the cell. It also keeps stuff in or out. You could say it works like screen a door. Perhaps a better analogy is that the cell membrane is like a border (between countries). The cell membrane (much like the border guards) control the traffic in and out of the cell. A fun answer could be to compare it to a Club bouncer, that allows certain people in and blocks the entrance of others. Another analogy for a cell membrane is that it is like a sieve. That is because it lets smaller particles (like water) in, while stopping bigger particles that could cause the cell harm out.
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