A semipermeable membrane, also called a selectively permeable membrane, is a barrier that lets some substances pass through it while blocking others. Whether something gets through depends mainly on its size, electric charge, and whether it dissolves in fats. Every living cell is wrapped in one: the plasma membrane, a lipid bilayer that lets small uncharged molecules such as oxygen and carbon dioxide diffuse straight through, while ions and many polar molecules need special protein channels or carriers.
This selectivity is what drives osmosis, the movement of water across a semipermeable membrane from where there are more free water molecules to where there are fewer. According to OpenStax Biology, a cell whose membrane lost this selectivity could no longer sustain itself. People also make artificial semipermeable membranes, for example in kidney dialysis machines and reverse-osmosis water filters.
Source: OpenStax Biology 2e, 5.2 Passive Transport
Image: Semipermeable membrane by Adam Rędzikowski, CC0, via Wikimedia Commons.