Constant Dollars: weighted by a constant/unchanging basket/list of goods and services.
Chained Dollars: weighted by a basket/list that changes yearly to more accurately reflect actual spending. The basket is an average of the basket for successive pairs of years; example of paired years are 2010-2011, 2011-2012, etc.
The technique is so named because the second number in a pair of successive years becomes the first in the next pair. The result is a continuous "chain" of weights and averages. The advantage of using the chained-dollar measure is that it is more closely related to any given period covered and is subject to less distortion over time.