Space is infinite, the universe (or rather the energy and matter within it) is only effectively infinite.
Allow me to explain. The universe (according to popular theory) started when a single point of intensely compressed energy and matter exploded, the big bang.
This has caused the universe to expand at the speed of light at its edges. Since it is (alledgedly) not possible to travel faster than light, it is therefore not possible to "catch up" with the edge if you were to attempt to reach it, hence the universe appears to be infinite.
If you want the real headfsck, comprehend this:
If the universe is effectively infinite, and the number of matter/energy combinations that can create life is finite, then this means that somewhere else in this universe are clones of all of us having this exact same discussion.....