The large Praying Mantis (not 'Preying' although it does that very well) got its name from the position of its forelegs. When resting, these front legs are held in a way that makes them seem folded in prayer. Those powerful front legs are able to hold down an insect as the mantis eats it alive. The mantis' mouth parts are capable of cutting through the tough exoskeleton of their insect prey.
Females lay their flat, seed-shaped eggs on a twig in autumn. The freshly laid eggs are then coated with a hard foam that maintains moisture during dry winters and deters birds and other insects from bothering them as well. In spring, the eggs hatch and pale nymphs, shaped like miniature adults emerge and immediately begin feasting on smaller insects and sometimes each other.
Mantises are extremely beneficial in gardens. They eat a large volume of pest insects and can be a farmer/gardener's best friend by removing infestations of wasps and beetles. A Praying Mantis (or its eggs) can be purchased in the spring and released onto a plant in a garden in order to head off any pests that arrive before summer. Larger species of the Mantis family have even been known to eat frogs, lizards and sometimes even hummingbirds.
Catching a glimpse of a Praying Mantis is a special thing, but leave it where you found it (if it hasn't flown away). It does a great service for growers, so for the benefit of the ecosystem, consider just admiring them, and capture only their photograph.