Griffins

The griffin, griffon, or gryphon (Latin: gryphus) is a legendary creature with the body of a lion and the head and wings of an eagle. As the lion was traditionally considered the king of the beasts and the eagle was the king of the birds, the griffin was thought to be an especially powerful and majestic creature. Griffins are normally known for guarding treasure and well valued priceless possession. One classical folklorist propounds the griffin was an ancient misconception derived from fossilized remains of the Protoceratops found in conjunction with gold mining in the Altai mountains of Scythica, in present day southeastern Kazakhstan.

In antiquity it was a symbol of divine power and a guardian of the divine.
Most statues have talons, although in some older illustrations it has a lion's forelimbs; it generally has a lion's hindquarters. Its eagle's head is conventionally given prominent ears; these are sometimes described as the lion's ears, but are often elongated (more like a horse's), and are sometimes feathered. The earliest depiction of griffins are the 15th century BC frescoes in the Throne Room of the Bronze Age Palace of Knossos, as restored by Sir Arthur Evans. It continued being a favored decorative theme in Archaic and Classical Greek art. In Central Asia the griffin appears about a thousand years after Bronze Age Crete, in the 5th-4th century BC, probably originating from the Achaemenid Persian Empire. The Achaemenids considered the griffin "a protector from evil, witchcraft and secret slander".
The modern generalist calls it the lion-griffin, as for example, Robin Lane Fox, in Alexander the Great, 1973:31 and notes p. 506, who remarks a lion-griffin attacking a stag in a pebble mosaic Dartmouth College expedition at Pella, perhaps as an emblem of the kingdom of Macedon or a personal one of Alexander's successor Antipater.

Infrequently, a griffin is portrayed without wings, or a wingless eagle-headed lion is identified as a griffin; in 15th-century and later heraldry such a beast may be called an alce or a keythong. In heraldry, a griffin always has forelegs like an eagle's; the beast with forelimbs like a lion's forelegs was distinguished by perhaps only one English herald of later heraldry as the opinicus.

Weakness
Well that depends on what kind of griffin you're talking about. If you mean a normal griffin, it can usually be killed by beheading, any type of fatal wound by a weapon, drowning (that's very hard), burning (that's very hard too), etc.
Traditionally in most legends, griffins are not assigned any special powers or magical properties that would make them any different from the animals they are composed of and so they can be killed by conventional means, just like any other animal.