Transfer calipers are calipers which have a short 'leaf' or 'secondary leg' -- actually, a third leg -- which can be used to 'remember' measurements.
You might, in some circumstances, need to measure a distance that requires some adjustment of the calipers in order to get a fix on -- e.g., under the rim of an overhang. Normally this would make using the calipers rather difficult, as removing the calipers would lose your measurement. Never fear, transfer calipers have the solution!
In addition to the two usual legs, transfer calipers have a short, third leg that usually lies against one of the two long legs. When it is needed, it can be tightened using a lock nut, fixing it in place in relation to the opposite leg. The long leg which it usually rests against can then be moved as needed so that the calipers can be removed from the object being measured. Once away from the object, the released arm can be realigned with the secondary leg, returning it to the correct measurement.