Interface reset is the number of times the interface has been completely reset. This can happen if packets queued for transmission were not sent within several seconds, if a serial line a malfunctioning modem is not supplying a transmit clock signal, or if there is a cable problem. Sometimes interface resets can occur when an interface is looped back or shut down.
A transition occurs when the interface changes its state, such as when it goes from being down to initializing or from initializing to up. A reset occurs when the interface is kick-started. Interface resets don't represent hardware resets, but rather the number of times that the line protocol had to restart/renegotiate after a failure. That may be causually related to overloading the router as far as the number of "high-speed" interfaces, but if that's the case you should also be seeing overruns & underruns, which are the direct evidence of running out of bus bandwidth. The interface resets may well represent periods when the processor was stalled or maxed out long enough to let a line protocol fail.
