What do plants gain by attracting animals such as: yucca moth and yucca plant, wasp mimicry in orchids, and mistletoe dispersal by birds?
Plants have a disadvantage compared to animals when it comes to creating the next generation: Most plants cannot move very much. This means that finding a mate and sending offspring into the world must be accomplished in ways that are very different from the reproductive behaviors we see in the animal kingdom.
Pollination is the process by which plants mate. Each pollen grain contains sperm, which much reach the egg cells of the female part of a plant to create a seed (offspring). Some plants simply let their pollen travel on the wind, allowing pollination to occur by chance. However other plant species utilize helpers from the animal kingdom in the form of pollinators.
Plants that use an animal pollinator must attract the animal to several flowers, so the animal can get pollen on itself and then move to another flower of the same species and deposit that pollen on the stigma (the female part of the plant). One way this is accomplished is by advertising (pretty flower petals, sweet odors) and then rewarding the animal visitor in some way, such as offering a sweet drink of nectar; this is how your example of the yucca moth and yucca plant operates. An alternative, but less common, strategy is to fool the pollinator into thinking that it will get a reward when no reward is present. This is the case for the wasp mimicry; the orchid flowers in question look and smell exactly like a female wasp, and the male wasps are fooled into trying to mate with these decoys.
Additionally, many plants use animal services to help disperse their seeds farther afield. In this case the fruit is the reward; by eating a tasty fruit and getting calories from it, the animal also consumes the plant's seeds, which pass through the animal's digestive tract and are deposited elsewhere.