A longbow is a type of bow that is tall (roughly equal to the height of the person who uses it); this will allow its user a fairly long draw, at least to the jaw.
A longbow is not significantly recurved. Its limbs are relatively narrow so that they are circular or D-shaped in cross section. Flatbow

Flatbow

A flatbow is a bow with non-recurved, flat, relatively wide limbs that are approximately rectangular in cross-section. Because the limbs are relatively wide, flatbows will usually narrow and become deeper at the handle, with a rounded, non-bending, handle for easier grip...

s can be just as long; the difference is that, in cross-section, a flatbow has limbs that are approximately rectangular.

The longbow is based on the late medieval English longbow

English longbow

The English longbow, also called the Welsh longbow, is a powerful type of medieval longbow about 6 ft long used by the English and Welsh for hunting and as a weapon in medieval warfare...

 in use during the 12th to 16th centuries.
The historical longbow was a self bow

Self bow

A self bow is a bow made from a single piece of wood. Extra material such as horn nocks on the ends, or built-up handles, would normally be accepted as part of a self bow...

, often made from yew

Taxus baccata

Taxus baccata is a conifer native to western, central and southern Europe, northwest Africa, northern Iran and southwest Asia. It is the tree originally known as yew, though with other related trees becoming known, it may be now known as the English yew, or European yew.-Description:It is a small-...

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