Essentially, a Layer 3 switch that is capable of examining layer 4 of each packet that it switches. In TCP/IP networking, this is equivalent to examining the Transmission Control Protocol (TCP) layer information in the packet.
Vendors tout Layer 4 switches as being able to use TCP information for prioritizing traffic by application. For example, to prioritize Hypertext Transfer Protocol (HTTP) traffic, a Layer 4 switch would give priority to packets whose layer 4 (TCP) information includes TCP port number 80, the standard port number for HTTP communication.
Some vendors foresee higher-layer switches that examine layer 5, 6, or 7 information to provide more control over prioritizing application traffic, but this might be just vendor hype.