What does it mean to say "Yes. No" as a reply?

Question

People say “Yes. No” as a reply. I’ve heard it many times. For example, one man says,

I accepted Jesus Christ as my Lord and personal savior yesterday.

And the other replies,

Yeah. No, I saw that.

Can someone explain to me the meaning of "Yes. No"?

Answer 1

Especially pronounced yeah, no, this answer is

an agreement; the “yeah” functions as affirmation, while the “no” could be replaced by the phrase “don’t worry.” (Wikipedia)

The no can actually be interpreted also as, I get you, really, I do believe you, depending on context.

In a post on OUPblog, Professor Edwin L. Battistella (Southern Oregon University in Ashland) says:

“Yeah no” is what linguists call a discourse marker. Discourse markers are usually short and sometime vague-seeming parts of a sentence which serve semantic, expressive, and practical functions in speech. They can indicate assent or dissent (or sometimes both). They can indicate attention, sarcasm, hedging, self-effacement, or face-saving.

LanguageHat quotes Professor Kate Burridge from Monash University, Australia, giving a more systematic classification of uses:

Professor Burridge says the phrase falls into three main categories, each determined by context. The literal agrees before adding another point, the abstract defuses a comment and the textual lets the speaker go back to an earlier point.

Sarah Grieves lists 8 ways you can use the phrase, giving examples from The Spoken British National Corpus

Agreeing, Disagreeing, Partially disagreeing, Showing you’re listening, Introducing a new idea, Showing enthusiasm/emphasising, Hedging/hesitation, Clarifying (Cambridge.org)

This is spoken language, so the use of the expression will be very flexible, with a meaning sometimes not clear to the speaker himself. I personally use it sometimes, for example, to express that not everything is black or white, yes or no.

If you want to read more about it, there is plenty on this post from the LanguageLog.

Addition: I found an article about Yeah, no on Grammarphobia and I can't resist quoting it here:

Even presidents of the United States aren’t immune. When a radio interviewer in 2011 asked Bill Clinton how he felt about being spoofed on TV comedy shows, Ben Yagoda writes,

The former president replied, ‘Oh yeah, no I thought a lot of the Saturday Night Live guys were great.’ ”

Among other examples, the same article gives an example of the phrase being used to express agreement:

The lexicographer Jonathan Lighter quoted a former New York City police detective as saying on CNN:

Yeah, no, you’re right!

Lighter added:

There it seems to mean, ‘Yes indeed, and no, I wouldn’t think of contradicting you.’

Answer 2

It is quite common for responses in English, at least in American English, to contain an affirmative and a negative together. Example:

A. There's a concert in the park tonight. Do you want to go?
B. Yeah, no. I'm too tired.

In such an example, the first word is not really an assent or a confirmation. It is instead a way of saying, "Yes, I understand the situation." The subsequent negation asserts the negative polarity, rejecting the proposal.

Sometimes there will be a flavor of sarcasm to it, and sometimes even two affirmatives together will assert a negative. Example:

A. I saw an alien spacecraft land in a field north of town last night.
B. Yeah, right.

Here there is no doubt that B is contending that A is mistaken, joking, or crazy.