When a company completes a share-buyback it either retires the shares or parks them in treasury. Treasury shares sit on the balance sheet as a negative number inside equity. They can be re-issued later to fund employee grants or an acquisition without a new charter vote.
For traders, treasury holdings are latent supply. A company with a big treasury block can hand shares to a seller in a deal without going to market.
Example: a company repurchases 15M shares at an average $30, spending $450M. Outstanding drops from 200M to 185M. Two years later it re-issues 5M of them for an acquisition, and outstanding goes back to 190M.
Related: share-buyback, outstanding-shares, issued-shares, dilution