Damselflies are insect

Insect

Insects are a class of living creatures within the arthropods that have a chitinous exoskeleton, a three-part body , three pairs of jointed legs, compound eyes, and two antennae...

s in the order Odonata

Odonata

Odonata is an order of insects, encompassing dragonflies and damselflies . The word dragonfly is also sometimes used to refer to all Odonata, but the back-formation odonate is a more correct English name for the group as a whole...

. Damselflies are similar to dragonflies

Dragonfly

A dragonfly is a winged insect belonging to the order Odonata, the suborder Epiprocta or, in the strict sense, the infraorder Anisoptera . It is characterized by large multifaceted eyes, two pairs of strong transparent wings, and an elongated body...

, but the adults can be distinguished by the fact that the wings of most damselflies are held along, and parallel to, the body when at rest. Furthermore, the hindwing of the damselfly is essentially similar to the forewing, while the hindwing of the dragonfly broadens near the base. Damselflies are also usually smaller than dragonflies and weaker fliers in comparison, and their eyes are separated.
Zygoptera comes from the Greek

Greek language

Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...

 zygo meaning joined or paired and ptera meaning wings.