sent 4013337 bytes received 76 bytes 39934.46 bytes/sec
total size is 5171204259 speedup is 1288.48
rsync is telling you that it actually transferred 4013337 bytes (~4MB) from the local machine to the remote machine, and 76 bytes in the other direction. It gives you an average transfer rate, and then the big number, the size of the directory that was just synchronized - 5171204259 (~5GB). The speedup number represents the Total size divided by the total data transferred in both directions (TOTAL SIZE / (SENT + RECEIVED)) = SPEEDUP. This is better termed the "advantage" of using rsync, but the developers chose "speedup" and that's what we got. You could think of it as a ratio/multiplier, since a speedup of 1 would mean that you basically transferred the whole thing with no speedup, as opposed to that example operation, which transferred 1/1288 of the total data to make up the difference.
Registered Linux User #370740 (http://counter.li.org)