DAT addresses many of the problems associated with standard tape, but does not solve all of them.
Standard tape employs an analog method of recording.
That is to say, at any given time, the voltage coming off of the playback head in a tape deck may be any voltage within a certain range. This voltage directly represents the sound recorded on the tape. With DAT, what is stored on tape is a digital representation of the sound. However, it is not an entirely accurate representation of the sound, as there are a discrete number of representations for each sample. That is to say, where an analog signal can be any value in between two end points, a digital sample can only be one of several values in between those points.