Well, don't we all? By "all," I mean all living things that reproduce sexually. When you think of it mechanistically, an organism's adaptations are primarily directed toward getting its genes into the next generation. Eat, sleep, avoid predators, grow up and reproduce—what else is there? Well, besides keeping in touch through Facebook.
For dragonflies, it's a long larval life in the water, as they eat and try to avoid being eaten. Then the magic of metamorphosis when they leave the water to become an adult winged insect. After that, more feeding and predator avoidance and, most of all, attempting to reproduce.
Male dragonflies spend much of their time at the water. Think of a singles bar, where the males are hanging around in hopes of meeting someone of the opposite sex. That's why those males head for the water. As the larvae are aquatic, the females have to lay their eggs in the water. Because the females have to come to the water to do this, males have a better chance of meeting one there.
Because so many males are at the water, the sex ratio can be extremely skewed there, with dozens to even hundreds of males for every female. Thus for a male there can be extreme competition for mates, and some males never mate in their lifetime. One way to alleviate that is for a male to defend a territory large enough, keeping other males out of his air space, so that he has access to any female that approaches. Many kinds of dragonflies do just this.
When a male damselfly sees a female, he immediately attempts to grab her for mating. He flies up to her, lands on her head and bends his abdomen forward to clasp her "neck" (prothorax) in two pairs of clasping appendages at the end of the abdomen. As soon as he has a good grip, he brings his abdomen forward and transfers sperm from the tip of his abdomen, where they are produced, to a storage chamber called a seminal vesicle in his second segment. From there, the spermatozoa can be transferred to his copulatory organ.
He then signals the female his readiness to mate by swinging her forward. The tip of her abdomen contacts his second segment, and structures on both of them form a firm connection. His genital ligula (penis) then transfers the sperm to the female's vagina, where it is moved to the spermatheca, another storage organ.
They then disconnect from that point, and she is ready to lay eggs. Her eggs travel from her ovary down her oviduct and are fertilized as they pass the spermatheca. She then can insert them into plant tissue with a specialized ovipositor, and the cycle begins again.
Dragonflies do about the same thing as damselflies, but the male fills his seminal vesicle before mating, and he clasps the female's head with three clasping appendages. The majority of dragonflies lay their eggs directly into the water rather than inserting them into plant tissue. See Odonate Oviposition, November 3, 2011, on this blog site.