What term refers to a membrane-bound compartment with a specific function in cells?

The term that refers to a membrane-bound compartment with a specific function in cells is "organelle." Organelles are specialized structures within a cell that perform distinct processes essential for the cell's life. Examples of organelles include the nucleus, which houses genetic material, mitochondria, which produce energy, and the endoplasmic reticulum, which synthesizes proteins and lipids. The defining feature of organelles is that they are enclosed by membranes, allowing them to create distinct internal environments suitable for their specific functions.

In contrast, the other terms provided do not fit this definition. A cell wall is a rigid structure outside the cell membrane in plant cells, algae, and some bacteria, providing structural support but not functioning as a compartment for biochemical processes within a cell. Plasmids are small, circular DNA molecules found in bacteria that can replicate independently of chromosomal DNA, but they are not membrane-bound compartments. Vesicles are small membrane-bound sacs that transport materials within cells but are not classified as organelles themselves; they typically function as carriers for substances between organelles or to the cell membrane.