What are the function(s) of Alu elements in the cell?
Alu elements are a type of transposable element. They possess the means for their own duplication and movement.  Alu is a SINE-like element that is transcribed by RNA Pol III, and so a single DNA copy can make multiple RNA copies, each capable of inserting into DNA, so it's no wonder they have a very high copy number.  Here is a picture of one means of insertion http://www.nature.com/nrg/journal/v3/n5/box/nrg798_BX1.html, although there are likely others.

They do not have "a function" per se, in that they are not selected for, they are just rarely selected against and there are so many of them.  They do not add functionality, but rather are one half of the "war" between transposable elements and viruses versus the genome's evolution to mitigate the damage they cause.  They are, of course, commonly used as sources of new DNA for sequence evolution, or can be used to create transpositions or other chromosome rearrangements, but mostly they just fail to cause too much damage and so tend to accumulate in the genome.