Hi,
First of all you need to know what do we mean by L2/L3.
L2 - Layer 2This is also referred to as the OSI (Open Systems Interconnection) Data Link Layer. It provides the means for synchronizing the bit stream flowing to and from the physical layer and for the detection of errors due to transmission problems e.g. noise and interference. An example of a Data Link protocol would be Ethernet operating on a LAN (Local Area Network).L3 - Layer 3This is also referred to as the OSI (Open Systems Interconnection) Network Layer. It provides the paths for the transfer of data between systems and across networks. The paths between systems may include switched services and interconnections of multiple subnetworks on route. An example of a protocol operating at the network layer would be IP (Internet Protocol).
So L2/L3 testing means nothing but the network protocol testing of the devices such as either devices(network card), router and switches.
Please download the following ebook on network protocol testing to get a good idea on that.
http://rapidshare.com/files/369037088/Multilayer_Switch_Testing_and_Analysis.pdf
Hope this will help.
Thanks
Raj