Heres a simple definition:
First generation crypto currencies have very limited functionality, you can store and transfer tokens in a secure and stable manner, using the blockchain as a simple transaction ledger.
Examples are Bitcoin, Litecoin, DOGE.....and pretty much all of their clones.
Second generation crypto-currencies use the blockchain as not only a means of storage and transfer, but also to offer extra functionality, such as marketplaces, financial apps, colored coins......
Examples are NXT, Counterparty, Mastercoin,.....
Second gen currencies are more like financial eco-systems, built on a blockchain, using their own currency as fuel for their application systems.
Sounds right, but what would you call something like Bitcoin with Mastercoin or Colored Coins? Or Peercoin with Peershares? Sometimes a first generation coin can have second generation features layered on top of it.