Harry's Patronus Charm

A Patronus Charm is a spell used to ward off creatures called Dementors. It can also be used for communication among other things. Harry's Patronus Charm takes the form of a stag. When a wizard or witch becomes an animagi, generally they take the form of an animal that represents them in some way. When Harry's father became an illegal animagi, he took the form of a stag. So it's not surprising that Harry's Patronus Charm, which is a protection spell, would take the form of his father. Several cultures have different meanings for stags:

According to Celtic culture, the stag represents a powerful male and is the king of the forest because of his antlers. The stag loses and grows new antlers as the seasons change, symboling death and rebirth.

In Chinese culture, the stag is said to be the only being that has achieved immortality.

In Anglo-Saxon culture, the stag is a creature of peace and nobility. It is said it will only attack when provoked.

In Native American culture of North America, the stag (known generally as deer) is seen as a creature who walks in light, and is pure.