Could you please differentiate between Cost Centres, Cost Objects & Cost Units?

A cost object is whatever we are calculating a cost for.

For example, if I was a company making desks, then the cost object (or cost unit) would be one desk. It is the cost of one desk that I would need to calculate (so that, for example, I could decide on what selling price to charge).
An example of why a customer might be a cost object is that suppose you asked me to do a special job for you. I would need to calculate the cost of that special job so that I could decide what price to quote you. The special job (or you as the customer) would be the cost object.

When calculating the cost of a cost unit or object, we need to look at all the costs involved. If I was making desks, then there might well be several ‘departments’ involved – maybe in one department we cut the wood; in another we assemble the desk; in another we paint the desk. These would all be cost centres in that there will be all sorts of costs in each ‘department’. We would need to find the total cost in each cost centre first, and then we would start estimating a cost per desk. The wages of the manager of a department would be one of the costs of that cost centre.

It might help you to watch the free lectures on here – especially the one on ‘cost classification and behaviour’ and the one on ‘accounting for overheads’ (which is where cost centres become more important for the arithmetic).