As taught in basic biology classes, plants differ from animals in several substantial ways, including mobility. While animals are mobile and can choose their environment, plants are stationary, rooted in one place.
However, while this might be true for an individual plant, on a different level, plant do indeed move, just at a different speed and with unexpected parts.
While animals move their entire body, including all related organs, plants move only their embyos. Plants pack their embryos in a bag that is on the one hand resistant to environmental harshness, and on the other hand "opens" immediately to the right set of cues, which are a complex mixture of light, temperature and moisture. This package is of course the seed. This is the real moving part of the plant, moving sometime as far and as rapid as animals do, and even more.
Seed movement requires agents of transportation, and different types of seeds are adapted to different agents of transportation. These could be physical, such as wind, carrying light-weight seeds (sometimes equipped with wing-like appendices) to circle the globe like dust. Such are, for example, seeds of orchids. Animals, just to close the circle, are good transportation agents because they... well, move. Fury animals, like dogs and cats, are especially adept at transporting seeds, as so also are, surprisingly, (relatively) hairless humans. In place of fur, our clothes become the furry vehicle that seeds hitch a ride on. See the picture of my leg, my sock covered with seeds of Daucus carota (the wild carrot) and other seeds. All are spiny and adapted to catch the fur on my (or on other mammal's) leg.