In traditional implementations of proof of work, such as Sha256 and scrypt, the energy put into the network is spent solely on the creation of new currency units. In these single use scenarios the work done is typical not useful outside of determining ownership of newly created currency units. Energy-Multiuse networks are those that combine the act of creating new currency units with a secondary effect that typically provides some benefit.
Examples energy-multiuse networks include Primecoin. whose proof of work algorithm both plays the traditional role of security the network though transaction verification and currency distribution and also looks for specific prime chains. Another example is Namecoin. which uses its proof of work algorithm to provide distributed DNS services.