Question

What is the main purpose of summarizing the conversation with the client at the end of a meeting?

Answer 1

There may be various different purpose for summarizing the conversation.
In order to know whether or not client understand the objectives and result of the meeting.
In order to know confirm the agreements again.
In order to let every one again give the chance to give their point of views.
and also  to confirm when will be the next meeting held.
So, that final conversation could be made upon meeting end.

Answer 2

Summarizing the conversation at the end of a meeting helps to state the outcome more clearly. It helps to convey your terms more clearly to the client. It confirms the decisions taken during the course of the meeting and indicates what has to be done to achieve the goal. It helps to bring forth the salient points discussed in the meeting and the conclusions arrived at the end of the meeting. It acts as a reminder. It also helps to build the confidence of the client and makes him feel that he is cared for and that his needs have been noted and attended to properly.