The process of fertilization occurs in both plants and animals. There are, of course, differences in the details and mechanisms. On the other hand, some of the similarities are striking. For example, the moss plant has both swimming sperm cells and eggs. In the moss plant, fertilization occurs by the sperm swimming to the egg. Vertebrate animals also carry out reproduction by way of sperm and egg.
One of the differences between plants and animals in this regard is that plants are, for the most part, sedentary. The moss plant depends on rain or very wet conditions in order for the sperm to swim from the male parts of the plant to the egg in the female parts. In the case of animals, the male and female are mobile individuals that physically interact with one another in the process of mating.