This is summarised from Wikipedia. (i.e. I've tried to get rid of the 'sciency terms'!).
Protein electrophoresis is a process whereby blood serum (the fluid part of the blood) is placed into a gel and exposed to an electric current. That serves to separate out five key elements of the serum, which should produce a graph looking like this:
http://en.wikipedia.org/wiki/File:Serum_protein_electrophoresis_normal.PNG
If the albumin spike was much smaller than shown there it could be an indication of disease. However since a decreased spike is present in many diseases it simply alerts doctors to the need for further investigation, rather than telling them anything specific.
If the gap between the albumin spike and the one for alpha 1 is particularly high (as may occur with some liver problems) or low (as may occur, for example, during pregnancy) then it might also indicate some type of abnormality.
Similarly, variations in both the height of the peaks and of the gaps in between them, can indicate other types of medical irregularities, See here if you really want to try to make sense of it all ('cos I'm getting lost!):
http://en.wikipedia.org/wiki/Serum_protein_electrophoresis
The second test looks a great deal more complex to me but, basically, it looks for 'free light chains', which are partially-formed proteins that are
sometimes produced (rather than fully formed ones) when myeloma (a type of cancer) is present.
Well, I tried anyway!