It is difficult to say what multi-agent computing is, because the definition of an agent is usually very soft surrounded by markting terms etc. I'll try to explain what is it and where it could be used based on the research of manufacturing systems, which is the area, I am familiar with.
One of the "unsolved" problems of modern manufacturing is scheduling. When the definition of the problem is static, an optimal solution can be found, but in reality, people don't come to work, manufacturing resources fail, computers fail etc. The demand is changing all the time, different products are required (i.e. mass customization of the product - one produced car has air conditioning, the next one doesn't, ...). This all leads to the conclusions that a) manufacturing is very complex, b) static approaches, like scheduling in advance for a week, don't work. So the idea is this: why wouldn't we have intelligent programs representing parts of the systems, working the way out of this mess on their own? These programs are called agents. They should communicate and negotiate amongst themselves and make sure the tasks are done in due time. By using agents we want to lower the complexity of the control system, make it more manageable, enable better human - machine interaction, make it more robust and less error prone and very importantly: make the control system decentralized.
In short: agents are just a concept, but they are a concept everyone can intuitively understand. Code still needs to be written, but it is written in a different way, one abstraction higher than OOP.