The word "finite" means that something has limits or boundaries. It comes from the same root word as finish, as in the finish line in a race. When something is finite it means that if you go on far enough, you will come to an end. If there is no end, then it's not finite; it's "infinite".
Similarly, the word "eternal" means unbounded by time.
We can almost, but not quite, imagine something that is infinite and eternal. To think of something that is really really big, or that takes a really long time, isn't quite accurate, because we really need to think of something that transcends physical size and duration. But it's at least a start, in stretching our minds to consider what the nature of God could be.
Here we have a physical universe. It must have come from something. Plus, we have these glimpses that there are spiritual realities, too. Mathematics suggests that there are more "dimensions" needed to help make sense of the physical world. Some people have near death experiences. Some dying people seem to communicate with people who have already died. These things are at least suggestive that there could be an afterlife, and/or a spiritual plane of existence -- and that God exists.
In New Christian theology, we believe that there is an infinite, eternal God. He is Divine Love, which is the wellspring of everything, and Divine Wisdom, which gives form to that love. He is unbounded by space or time.
That conception might make God seem distant and impersonal, but logically, that doesn't need to be the case. An infinite God is "big enough", capable enough to be both creating and sustaining the universe AND flowing into each one of us in ways attuned to our ability to receive his influx. A God who has the perspective of eternity also has the ability within that to operate in our lives, in our time, even if we can't perceive it.
These concepts are at the limits of many kinds of thought - science, philosophy, mathematics, and religion. There IS an underlying harmony of those disciplines, but it's hard to see sometimes, particularly because we can be blocked by preconceptions and because we're operating with finite minds, wrestling with things that we can only really see appearances of.
(For reference, see True Christian Religion 27-33)
