The System.map file is a file that:

• Has versioning info
• Has a symbol table

Peter Jay Salzman has a great write up about this on his System.map page.

Also for an example of the symbol table run this command:
cat /proc/ksyms

You should get output that looks like:

[...]
c038670c br_handle_frame_hook_Rc7f936a5
c03884e0 br_ioctl_hook_R1fb9705f
c0388220 inetdev_lock_R8c3f0ef4
c0277dd0 inet_add_protocol_Rffd2c010
c0277e50 inet_del_protocol_R45af3a96
c029dc70 inet_register_protosw_R7d794405
c029dd30 inet_unregister_protosw_Rc94ba9e7
c0276490 ip_route_output_key_R9ebc1292
c0275c90 ip_route_input_R4a156743
c0299be0 icmp_send_R8f9041a6
[...]


Go read his write up about this mysterious file, he gives you great information about where to keep it, why you might need it and common problems related to System.map.