It will probably be easier to understand if you look at larger chassis (7600, 12k) and for example their SPA Interface Processor modules (SIPs) and SPA cards. Chassis have slots in which you can place designated hardware modules and those modules can have sub-slots. Keep in mind that some of this stuff can be integrated (probably the thing that is confusing you) or left for you to populate with desired hardware.
So in my example with SIP and SPA you will place SIP module in slot of the chassis, and then you place SPA cards inside sub-slots of the SIP.
In these configurations you will have interface names as:
In larger, high end routers, with IOS XR you can also see the chassis:
So the interface name describes the location of the interface from most significant part (slot in my example) to a least significant part (port in my example).