Mesosomes are an intracellular compartment (organelle) present in bacteria. These are generally more prevelent within Gram-positive bacteria as opposed to Gram-negative. They are thought to be formed through invagination of the cell membrane. 
Although once thought to be equivilant to mitochondria, no sufficient evidence has arisen to suggest that they present any unique function within the cell. Other membrane functions have been attributed to mesosomes, as their origin is thought to arise from membrane pertubation thanks to electron microscopy studies.