What does it mean to be clean in the context of the Old Law? In a large number of places, the books of Leviticus and Deuteronomy mention cleanliness, saying that certain persons or things are clean or unclean. I won't mention any particular passage because I would like a general explanation of the idea.

What does it mean to be clean or unclean in the context of the Old Law?

(An answer might talk about modern practices similar to this "clean/unclean" distinction, or Christian tradition in general.)
My understanding of cleanliness vs uncleanliness had to do with ability to participate in Jewish religious ceremonies.  They were things which were not sinful, however when made unclean, would make one ineligible to participate in Holy ceremonies.  The level of purification needed also scaled with the closeness to God, with a very large amount of purification prior to a high priest entering the Holy of Hollies.  It is my understanding that this view does not differ greatly from traditional Jewish views of Levitical cleanliness.