Concession is a conversational technique that people use when trying to persuade someone. Here's an example from a conversation between a car salesman and a customer:

This might be a little more than you wanted to spend, but if you think about the long-term value it's a great deal.

In this example, the salesman starts by giving a reason that the customer should not buy the car, but then ends with a reason why he should. Another example:

I know you're busy, but can you help me out with this?

In this case, the concession is "I know you're busy." Starting your request or argument this way shows that you understand the other person's point of view.