Paraproteins are an immunoglobulin (or part thereof) produced by a single type of clone from B lymphocytes. Because only one type of original cell is cloned many, many times, all of the clones will produce the same immunoglobulin. When plasma is then electrophoresed, the paraprotein shows up as a discreet, single, dark band. You could represent it graphically like this:
Paraproteins are common in multiple myeloma, solitary plasmacytoma and Waldenstrom's macroglobulinaemia, but they are found in other conditions too (e.g. some types of leukaemias and lymphomas).
In multiple myeloma, the light chain of the immunoglobulin is usually (75% of cases) secreted without the usual heavy chain. In around one fifth of cases, in fact, no full immunoglobulins are secreted at all, and only the light chain (called the Bence Jones protein) is secreted. The problem is that the light chain is rapidly cleared from the plasma, and so it doesn't show up in tests. Thus, if you're looking for multiple myeloma, always test the urine for Bence Jones protein, where it accumulates.