Asexual reproduction needs only one parent, unlike sexual reproduction, which needs two parents. Since there is only one parent, there is no fusion of gametes and no mixing of genetic information. As a result, the offspring are genetically identical to the parent and to each other. They are clones.
Asexual reproduction in plants can take a number of forms. Many plants develop underground food storage organs that later develop into the following year's plants. Potato plants and daffodil plants do this, for example.

A daffodil bulb at the beginning and end of the growing season, with a lateral bud where the new plant will grow

Strawberry plant with runners - stems growing sideways
Some plants produce side branches with plantlets on them. The spider plant, Chlorophytum, does this. Other plants, such as strawberries, produce runners with plantlets on them.
Asexual reproduction in animals does occur - it happens in sea anemones and starfish, for example - but it is less common than sexual reproduction.
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