The word “infinite,” in Christian theology, has meant “without limit.” “Eternal” means everlasting, without end. We are eternal, but only God is infinite. Infinity is one of the incommunicable attributes of God. That is one which we as humans cannot share in. As the Creator, He is infinite. As His creatures, we are finite, and all that we do is finite.
For more information on this subject, see Randy Alcorn's book Heaven.