DDR is an acronym for Double Data Rate and is a class of memory used in computers. The functions of all DDR classes is to increase bandwidth in data transfer. Here's some history.

Because of its impracticability to mass produce DDR in excess of 400 MHz, DDR2 was designed. However, in its debut, DDR2 had only two clock rates, 200 and 266 MHz. Despite being worse than DDR, DDR2 became increasingly popular due to lower latency modules became available. DDR3 hit the market sort of as a requirement, due to the new technology of the Phenom II and I7 CPUs. These CPUs were designed with internal memory controllers.

The basic gist of it all is that each newer class supercedes its previous (DDR3>DDR2>DDR) because of their respective benefits, the most widely known is the data rate transfer. Neither of the classes are, backward or forward compatible. That is, if your mobo specifies use of DDR2, you can't use DDR or DDR3. Though the pin allocation is the same in DDR2 and DDR3 (240 pins), forcing one into the other would result in damaging the DIMM socket.