Difference in meaning between sentences.

The difference is specificity on when the meeting happened. Is that not obvious?

No, the difference is not obvious, especially for an ESL.

Adding the "specificity" makes it even less obvious.

Advice on language should be adapted to the level of the question asked.

I have met her is a sentence using the present perfect tense. This means we cannot know when the subject of the sentence met the object. In fact, specific time markers like today and yesterday would be incorrect if added to the end of a sentence in the present perfect. Time markers, however, that aren't specific like once and before, which show how frequently the subject has met the object, are fine. All we know from the sentence you have given, I have met her, is that the subject, I, has met the object, her, at some point in time. That could be 30 years ago or an hour ago.

I met her today is a sentence using past tense. This means the meeting between the subject and object happened sometime earlier today. We cannot know when exactly from the sentence but we do know they met today. In the other sentence, we don't know that.

Thanks, perennialloner, for your cystal-clear detailed reply.

Apologies of my reply seemed rude but your use of English seems quite advanced (ie "crystal-clear detailed reply"). And may I ask, is the term "specificity" less easy for you to understand than "present perfect tense"?

Thanks, blatham, for the compliment.
The word "specificity", to me, doesn't drive home the point that the sentence in the present perfect tense.
Perennialloner's explanation is detailed and easy to understand.

That's very interesting. What is your native language and how are you going about mastering English?

I have used British English since I was a child. It's not easy to master English, which I learn every day. I believe learning is a daily process. In this way, I hope to have a good command of English. At this stage I think my English is mediocre, at best.

What about you? Are you a native speaker of American English? Or a British English native speaker?

Your written English is very good. I'd have no reason to guess it wasn't your first language. Your sentence structure and even your punctuation is quite proper and careful.

I'm Canadian so my English is closer to how Americans speak and write (Canadians and Americans share many more idioms than either of us do with the British). In the US there is quite a range of accents but that's much less true in Canada where only Quebec and the Maritime provinces show considerable local variation.

Thanks again, blatham, for the following kind words.

Your written English is very good. I'd have no reason to guess it wasn't your first language. Your sentence structure and even your punctuation is quite proper and careful.

Hehehe!