Hypothecation is the posting of collateral to secure an obligation. Rehypothecation is the reuse of posted collateral. For example, if an institution receives collateral from a counterparty to secure an obligation, that institution may rehypothecate the collateral by lending it, repoing it, or posting it as collateral for one of its own obligations to a third party.
Rehypothecation is not permitted in some jurisdictions. It is common practice in the United States. Any collateral agreement should explicitly permit or not permit rehypothecation.