In some mythos that is correct. For example in Hinduism it is the physical incarnation of a deity in the “real world” i.e. come down from heaven.
When I was younger I used to explain (to others bewilderment) that both Jesus and The Holy Ghost/Spirit were avatars of God (the Father) or Creator. Jesus being the physical avatar and the Holy Spirit/Ghost the astral projection/spiritual avatar. The latter also being consistent with the HS being the “Word Of”
However, in other mythologies and many Fantasy/SF books it is a god’s representative.
As I have defined it here, I use the broader Fantasy/SF literature version.
So in Astlanian terminology an avatar is either a Saint, Archon, Angel, Prophet, etc. Someone that acts with the deity’s authority.
Now of course, this is (could) also (be) an Apostle, Emissary, Ambassador, Agent