Some residencies do not start at year 1 but instead at year 2 and are called things like 2,3,4 programs (eg some emergency medicine residencies). You then do a 1st year either there or somewhere else. This is the 'transitional year'. I think it's most often asscoiated with trying to get into a radiology or opthamology program where you need a first year rotating through general rotations before specializing. I think some people who do this already have a residency to go to after the transitional year, some people do it because they didn't match and will try to match into a 2,3,4 /whatever the next year.
...hope thats not too confusing...basically there are a series of situations thats can lead someone to be doing a 'transitional' year. It's just a first year not part of the full residency which takes you through various services.