A Line Replaceable Unit is a piece of hardware that can be exchanged for a replacement part in a relatively short time by only opening and closing fasteners and connectors. You will find the term LRU in avionics but also in ATC hardware. Examples are FMC, transponder, etc.
When you have a complex avionics system you tend to end up with a great variety of LRUs. All these LRU have a very specific function. To be able to quickly replace malfunctioning parts, maintenance needs to keep a large stock of spares for all these LRU's.
The Integrated Modular Avionics concept attempts to reduce the variety of LRU's by designing the avionics with common components. E.g. one type of power supply, one type of memory unit, one type of processing board and only a few variations of input/output modules. Instead of working with very function-specific LRUs, the IMU works with more generic Line Replaceable Modules (LRMs). This reduces the number of replacement parts that need to be kept on stock. The LRMs of IMA have more generic functions than in a traditional avionics system.
An IMA is a computer network utilising the ARINC bus system that interconnects various devices. This is in contrast to Line Replaceable Units LRU'S where they are standalone systems that can be replaced. Basically they are electronic boxes typically in the aircrafts electronics bay that can be swapped out quickly. Because they can be swapped out quickly they can be done on the line. Ie. When the airplane is on the tarmac or in the hangar