Onboarding is everything that happens between agreeing to start and being properly up and running. For a new customer it might be collecting details and agreeing a plan; for a new starter it is accounts, training and introductions; for a new system it is set-up and migration.
A clear onboarding process gives people a good first impression and stops things being forgotten. Written steps, named owners and a checklist mean the process does not rely on one person's memory. It is also easy to measure how long it takes and where people tend to get stuck.