There is also an official answer - courtesy of ITIL and the BS standard in IT Service Management (BS15000).
1st line support is where the people who answer the phones are able to supply an answer immediately. If they cannot do so, the incident is placed in a queue to be handled by the more technically aware 2nd line support. However, there are those problems which defy in-house technicians who then have to call on suplpiers for assistance (3rd line support). So there you have it. But don't EXPECT this level from any IT suppliers and consider yourself VERY LUCKY if you do get it. This is typically for organisations providing IT support for their own computer systems users, and is very expensive to provide.