Sexual reproduction, something that is more familiar to humans as it is how humans replicate, requires two parents (or gene sources) contributing genetic information to an offspring that will be unique. Gametes are the cells involved in this. The offspring, while having traits from both parents, will also have unique traits on the basis of genetics. Meanwhile, some species reproduce asexually. A key difference between sexual and asexual reproduction is that the offspring resulting from the latter is genetically identical to the parent - i.e. it is a genetic clone of the parent.
An advantage of asexual reproduction has been in agriculture. It allows for larger and faster production, and since the resulting offspring are identical to the parent, parents with desirable traits can be cloned. However, this can be disadvantageous in the case of a mutation as the entire set of clones can be terminated.
There are various ways to reproduce asexually. There is binary fission, budding, spore, fragmentation, agamogenesis (no male), parthenogenesis.
For potatoes, they reproduce sexually naturally via pollination by bees between potato plants. They also require seeds, the cells involved for sexual reproduction in plants. Meanwhile, potatoes can also be grown asexually through vegetative reproduction. This can be done, for potatoes, but planting a part of it (e.g. half a potato) and growing it. The result will be potatoes genetically identical to the parent potato. This is similar to budding (except potatoes are tubers), where an offspring grows from an existing root stem.
Potatoes can be reproduced asexually through vegetative reproduction (similar to budding).