Slumber means "sleep" — as a verb or noun. If you're a sound sleeper, you might slumber peacefully right through a thunderstorm, your slumber undisturbed.
To slumber is to sleep, sometimes specifically to sleep lightly or doze. You can slumber in your bed, in your airplane seat, or through your alarm in the morning. Slumber can also describe a peacefulness, like your quiet street that seems to slumber early in the morning. The phrase slumber party was first used in the 1940s to mean a gathering held at night, that usually involves very little slumbering.