CDA files are not, strictly speaking, a file at all. Taken more accurately they resemble Microsoft's shortcut files in that they point to information rather than containing it themselves. In the case of a shortcut, this means a pointer to a file somewhere on your computer, a .CDA file serves the same purpose for an audio CD and simply points to the track and sector on a disc where a song begins.
When you browse an audio CD using Windows, you'll notice that it appears to contain a directory of .CDA files and double-clicking on any given file will play the relevant track. Copy the file to your hard disc and then remove the CD, however, and it's a different story. At best, the player will report that the relevant CD is not present; at worst it will play from the same point on whatever CD happens to be in the drive at the time.
When Audiotools is used to read a CDA file, it first ensures that it is reading the correct CD, then rips the relevant track from the CD using the CD ripper engine. See CD Ripping for more details.
Rip the audio CD tracks you want to wav files then compile a audio CD in Nero.