In asexually reproducing organisms variation occurs due to inaccuracies in DNA copying at the time of nuclear division.
For example, one bacterium divides, it will give rise to two bacteria. These daughter bacteria would be similar in body design, but with subtle differences.[See Fig.]

Fig. Appearance of variations over succeeding generations
The resultant bacteria divide again, and each bacterium will give rise to two bacteria in the next generation i.e., there would be four individuals as shown in Fig. (iii). In the bottom row i.e., Fig.(iii) the four individuals will be different from each other.
They may have differences of two types (i) some of the unique type of differences and (ii) differences inherited from, their respective parents, who were different from each other.