Vesting of shares is when a person earns his right to ownership in the company by continuously working over a period of time. And a Cliff is the minimum duration one needs to work to own any shares at all.
These concepts are prevalent for ESOPs and funded startups. However, they hold equal or probably more importance in bootstrapped businesses where say, two friends get together to start a venture.
Only if partners in non-funded businesses were to also be aware of how to use these tools to their benefit to avoid future conflict and get equal commitment from partners to work, would business (maybe, hopefully, by a little bit, or a lot) have one less of a problem to deal with.