This is the date on which you usually move in to the new property (or at least the date you are entitled to do so!)
This date will have been agreed with you prior to exchange of contracts.
In some cases, it is possible to exchange contracts and complete on the same day, as long as all necessary arrangements for removals, mortgage funds, and any other money needed from you have been dealt with well in advance.
Usually, though, exchange of contracts and the completion date will be a few days apart.
If you are buying a brand new property then you may find that the developer requires you to exchange contracts weeks or even months before the property is ready to be lived in.