The seeds are carried inside the fruit by animals called dispersers. The animal usually feeds on the fruit (ovary wall), but "tosses" the seeds (or passes them through its digestive system). This assures that seeds end up far away from the "mother" plant, where they can develop without competition from "mom." The fruit may possess special characteristics to attract and encourage dispersal by an animal. Other seeds may be dispersed by catapult (as you observed in the arboretum walk), parachute, or other means. Once dispersed, a seed needs to germinate and grow into a new plant, eventually maturing into a reproductive adult plant.
Some seeds sprout with just water and reasonably warm temperatures. This is true of most common garden plants. Such seeds are often referred to as "seeds lacking dormancy." Wild species usually have some kind of deeper dormancy to avoid sprouting in late summer/fall when the seeds are dispersed. This assures that tender seedlings are not frozen at a young age, but do not appear until warm weather arrives in springtime. For these species it takes something more than just water and warmth to germinate.
The mother plants of our "wild" species put their embryos into dormancy by using chemicals. Perhaps in hardy plants the vast majority use abscisic acid to keep their embryos from germinating too early. This chemical is broken down by enzymes in the embryo over time. The enzymes have a cold temperature optimum. Thus the enzymes are not active until early winter. The abscisic acid keeps the embryo dormant from dispersal to frost. After 6 weeks at about 4° C, the optimum for the enzymes that metabolize abscisic acid, the AbA is metabolized completely. But now the cold soil keeps the embryo dormant until the warmth of spring (20° C). It is an ingenious mechanism evolved in hardy plants. To accelerate this process artificially, seeds of wild plants can be harvested in late summer as they mature, placed in moist soil, and kept in a refrigerator (4° C) for four to six weeks. This treatment is called stratification. After the stratification is complete, then the plants are removed to a lighted greenhouse that is reasonably warm. This treatment is called vernalization. Now the seeds will have "experienced winter and spring" and will germinate.
Some other wild seeds have very thick seed coats that are thoroughly lignified and waterproofed. These species have evolved the ability to pass through the digestive system of an animal or survive pounding in the surf at the shore or go through a fire before they are even able to sprout. The degradation of the seed coat is called scarification, and this process permits water to pass through the seed coat so that the embryo can begin metabolism, elongate its radicle, and germinate. Many wild legumes, such as the Kentucky Coffee tree and the Sea Bean, have such heavy seed coats.
Yet other wild seeds have an exceedingly thin seed coat. The evolution of the thin coat is accompanied by dormancy that is overcome by either light or darkness. The light can penetrate the seed coat and the embryo inside can then detect whether it is deeply buried or right on the surface of the soil. Small seeds with thin seed coats often require light for germination; large seeds with thin seed coats often require darkness before they initiate germination. Think about the amount of storage materials in the seeds and the evolution of the two different signal responses will become apparent. Examples of seeds requiring light include lettuce, seed requiring darkness include garden pea.
Some very small seeds may have a very rudimentary embryo (only a few cells large) and almost no storage material. The orchids you observed in the arboretum are an example. These seeds will not germinate until they are allowed to develop further. The seeds in nature are dispersed into soils that have symbiotic fungi. These fungi degrade detritus in the leaf litter and nourish the orchid embryos in the dark. Once the embryo has "after-ripened" to some sufficient stage, it will germinate and grow into an adult orchid plant.
Seeds of desert species (30 N and 30 S latitude) often have no winter cold signals, few animals for scarification, no fungi for nourishment or degradation, etc. These species often experience a dry season and a wet season in their environment. Not surprisingly desert species have evolved ways to ensure that their seeds sprout only when the wet seasons has arrived. Desert plants invest their seeds with phenolic substances that inhibit seed germination. As long as they are dry these seeds will not germinate. If there is a passing shower during the dry season, some of the phenolic is dissolved and leached out of the seed. But one shower is not enough...there is still enough phenolic left in the seed to prevent germination. After repeated rinsing, the phenolic is sufficiently leached out so that the seed sprouts during a bona fide wet season.
Shown below is the biochemical mechanism for seed germination in two species: barley and lettuce.