The Science Learning Hub of New Zealand offers this excellent answer to the question.

Plants cannot walk around and take their seeds to other places, so they have developed other methods to disperse (move) their seeds. The most common methods are wind, water, animals, explosion and fire. 

Wind dispersal

Have you ever blown on a dandelion head and watched the seeds float away? This is wind dispersal. Seeds from plants like dandelions, swan plants and cottonwood trees are light and have feathery bristles and can be carried long distances by the wind. Some plants, like kauri and maple trees, have ‘winged’ seeds. They don’t float away but flutter to the ground. With wind dispersal, the seeds are simply blown about and land in all kinds of places. To help their chances that at least some of the seeds land in a place suitable for growth, these plants have to produce lots of seeds.

Water dispersal

Many plants have seeds that use water as a means of dispersal. The seeds float away from the parent plant. Many aquatic plants and plants that live near water have seeds that can float, and are carried by water.  Plants living along streams and rivers have seeds that float downstream, and therefore become germinate at new sites.  The size of the seed is not a factor in determining whether or not a seed can float.  Some very large seeds, like coconuts, can float.  Some small seeds also float.

Animal dispersal

Birds often fly far away from the parent plant and disperse the seeds in their droppings. Some seeds have hooks or barbs that catch onto an animal’s fur, feathers or skin. Plants like pittosporum have sticky seeds that can be carried away by birds. Humans can also spread seeds if they get stuck to our clothing or shoes – and if we throw fruit pips and stones out of the car window!

Fire dispersal

There are some species(Abbreviation sp. or spp.) A division used in the Linnean system of classification or taxonomy. A group of living organisms that can interbreed to produce viable offspring. of pine tree that require the heat from a fire before their cones will open and release seeds. The intensity and timing of the fire is important. It needs to be hot enough to trigger the cones to open, but if fires are too frequent, there is not enough time for the plants to grow big enough to make new seeds.

Adaptation and seed dispersal

Adaptation is an evolutionary process that helps an organism make the most of its habitat. Seed dispersal is an example of adaptation.