It used to have more significance than it has now.
If you are concerned about long distance telephone charges, keep in mind that today many local telephone companies (the Baby Bells) offer long distance service and long distance carriers carry local calls so the LATA is not as significant anymore.
IMHO, what really matters is the overall rate plan for all toll calls (short distance and long distance) that you make.
A very brief definition would the boundary between a local and long distance calling area. Calls within a LATA were handled by your local company (even if toll), calls between LATAs were handled by your long distance company.
The front of your telephone directory should have a LATA map.
However, there were numerous exceptions right fromt the start. As mentioned, long distance companies now carry local calls and local companies now carry long distance calls.
LATAs may contain multiple area codes, or split up area codes. LATAs may span multiple states or be within a state.