In cell biology and protein biochemistry, heterologous expression means that a protein is experimentally put into a cell that does not normally make (i.e., express) that protein.  Heterologous (meaning derived from a different organism) refers to the fact that often the transferred protein was initially cloned from or derived from a different cell type or a different species from the recipient. 
Typically the protein itself is not transferred, but instead the correctly edited genetic material coding for the protein (the complementary DNA or cDNA) is added to the recipient cell.  The genetic material that is transferred typically must be within a format that encourages the recipient cell to express the cDNA as a protein (i.e., it is put in an expression vector). 
Methods for transferring foreign genetic material into a recipient cell include transfection and transduction.  The choice of recipient cell type is often based on an experimental need to examine the proteins function in detail, and the most prevalent recipients, known as heterologous expression systems, are chosen usually because they are easy to transfer DNA into or because they allow for a simpler assessment of the proteins function.