A composite transposon is a segment of DNA which contains the insertion elements at either end but can contain just about anything in the middle (genes, markers, etc.)
These types of transposons tend to be very large, and many of them are created when the inner two insertion elements of two smaller transposons stop working and only the two at the far ends continue to work, so that when the transposon moves, it takes everything in between the two original transposons with it.
Some composite transposons are used in genetics experiments; Tn5 and Tn10 are two such composite transposons which have genes that encode resistance to certain antibiotics.
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.