How we change what others think, feel, believe and do
Summarizing involves paraphrasing or otherwise repeating what has been said in a significantly shorter form.
Summarizing what you said
The person speaking may summarize what they have just said, in order to emphasize the key points.
Summarizing what they said
They may also summarize what the other person has said, in order to show that they have understood and to allow the other person to correct that understanding.
In other words, I believe we need to take action now and I think Jim should lead the project team.
So what you are saying is that you are going to write a report on the economy and deliver it to Sue at the end of the month. Is that right?
Let's check what we have decided. You are cooking tonight and I will cook for the rest of the week. Is that right?
We seldom remember everything that is said by other people (let alone ourselves), so a summary can be a useful way of encapsulating the key points. This allows the fuller argument that
Summaries can be given at the start ('This is what I'm going to tell you') although they more often are used afterwards ('This is what I've told you'). Using both can be a powerful method, especially if you have time to do this.
When giving a summary, it can help to say that you are about to do this. If people may have not understood what you have said this gives them a chance to catch up on the key points.
People doing presentations often deliberately summarize what they have said with the aim of ensuring people remember key points. The same principle applies in everyday conversation.