A polytene is a giant chromosome which is composed of thousands of copies of DNA parallel to one another instead of the usual one copy of DNA per chromosome. They are found in the salivary glands of insects, in certain protozoans, and in flowering plants.
They are also found in the larvae of the fruit fly Drosophila melanogaster and are useful to geneticists because all of the details of the fly's genetic structure are greatly enlarged.
Polytenization is a process where many copies of a set of chromosomes are made without separating the copies from one another.
The information in this writeup was taken from the science dictionary at http://biotech.icmb.utexas.edu/; I oversaw the development of the dictionary (the website was mothballed in 1998) and I believe I wrote the entry this is based on.