the matrix - What was the purpose of the medical check-up the Oracle performed on Neo?

When Neo goes to the Oracle for the first time, she performs a sort of medical check-up on him...

Oracle: Well, let's have a look at you... Open your mouth. Say, 'ahhh.'

She checks his throat, his ears, and do some kind of hand reading...

Was she just acting, trying to mess with Neo's mind, like telling him he was not the One? Or did it really have a meaning, programmatically speaking?

Answer

There's no special meaning to it. She's just playing out a sequence whereby she "examines" him and determines that he's not The One. After she examines him she says:

Oracle: OK, now I'm supposed to say, "Hmm, that's interesting, but... " then you say...

Neo: ..."but what?"

Oracle: But... you already know what I'm going to tell you.

Neo: I'm not The One.

It was just a way for her to act out a sequence so that Neo would jump to the conclusion that he wasn't The One. Neo wasn't The One yet* because he didn't believe it (that was the point about him breaking the vase, "know thyself", etc.).

How do we know the physical examination was unnecessary? The Oracle already knew Neo was The One before she touched him. We know this because she says

You're cuter than I thought. I can see why she likes you.

before she examines him. She is referring to Trinity, and she had already told Trinity that Trinity would fall in love with The One. She already knew Neo was The One (but "lied" to him) so the physical examination was unnecessary.

*Actually, The One carries code that must be re-inserted into the Matrix so in that sense Neo was always The One. But the Oracle tells us how important it is to "know thyself" and since Neo didn't know it he was not yet on the Path of The One.