An INS is a self contained navigation system in a box. It measures acceleration and vector and has a computer to direct the pilot along a pre-loaded flight path. The INS is a relatively old technology that is very expensive to maintain. The reason for triple INS' was that if you only have one and it started to drift you don't know it. If you have 2 INS' and one starts to drift, you won't know WHICH one. With three, you take the two that are closest together as the correct ones. Triple INS' have algorithms to update and "triple mix" the position to come up with the most likely accurate position.
An IRU is an Inertial Reference UNIT. They are typically much more reliable and simple than INS', but also use three for the same reason as the triple INS setup. It also measures acceleration and vector, but only keeps track of the present position, velocity, vector, and attitude of the aircraft. It does not itself have a self-contained navigation computer. In aircraft that use IRU's, there is another computer called the FMS, or Flight Management System. This is the navigation system similar to that integral to the INS box. A FMS also does many more things than an INS, such as fuel computation/predictions, temperature displays, etc. The IRUs simply provide the constantly updated position, speed, and vector of the aircraft to the FMS', which then do all the number crunching to navigate the aircraft.
Since both INS' and IRU's do "drift" slightly, various forms of updates can be provided to bring the system accuracy back. INS' typically use updates from DMEs. IRU's also use DME updates but many use GPS now also.
Hope that's clear.