Mosquito hawks are colloquial terms for crane flies and dragonflies. These insects received this nickname because they are perceived to eat mosquitoes, making them a beneficial insect. While it is true that the dragonfly eats mosquitos, the crane fly does not eat mosquitos (though the crane fly has no harmful effects on humans, so this insect is neither a nuisance nor a particularly helpful insect).
Mosquito hawks also received the term because they look like an oversized mosquito. This is particularly the case with the crane fly. The image to the left is a crane fly.
While crane flies do not bite humans, they are potential threats to your lawn in large numbers. Here is a useful Crane Fly FAQ.