I wonder if there any nuance between the two sentences.
- I admit that you are right.
- I concede that you are right.
I believe there is a slight difference between them. Do both sentences suggest that the speaker is in the wrong?
Okay then, I'll base my own answer simply on an analysis of the currently accepted answer.
The key sentence in the accepted answer (I admit that you are right suggests that the speaker wasn't agreeing with the second person's opinion but now admits or accepts openly that the second person is right) is simply wrong.
I will concede that 'admit' is admittedly the basis of the definition of 'concede'. But I will not admit that 'admit' itself necessarily implies the existence of a prior dispute. 'Concede' does carry that implication, but the difference between them is that 'admit' does not.
If you appear in a criminal court, you will be asked, firstly, to enter a plea: to plead guilty or not guilty, to state whether or not you admit the charge. The court will ask this on your first appearance before it, even though you have not previously had an opportunity to deny the charge. At this first hearing you can only either admit or deny it. If you deny it, then at a subsequent hearing you might change your mind and opt to concede defeat by changing your plea.
'Admit' does imply some consideration has taken place before speaking out, but it does not carry an additional implication that the speaker has disputed the facts prior to speaking. To maintain the fictional court setting: it is possible to admit the charge at the first hearing, by pleading guilty, an admission necessarily not requiring that you had disputed your guilt previously, since the charge had never previously been put to you.
There is nothing to concede, if you initially do plead guilty, since concede does carry an implication: namely that the speaker had previously made a false - or, at least, an inconsistent - statement (had, for instance, previously entered a plea of 'not guilty', knowing it was not true).
'Concede' implies a change of mind. 'Admit' only implies a making-up of one's mind. The distinction is between making a decision and changing a decision once made.
Let me improve the answer given by user18593
Checking Oxford Dictionary, you can find
Admit or agree that something is true after first denying or resisting it.
Origin: Late 15th century: from French concéder or Latin concedere, from con- ‘completely’ + cedere ‘yield’.
Confess to be true or to be the case
Origin: Late Middle English: from Latin admittere, from ad- ‘to’ + mittere ‘send’.
concedere: completely yield (see above)
mittere: send; but also tell, report
So, user18593 is right. concede implies that the speaker first denies something. admit does not contain that information, the speaker is just stating something to be true, maybe or maybe not previously such truth has been denied.
Yes, there is a difference between the two sentences' meanings.
The first one, I admit that you are right, suggests that the speaker wasn't agreeing with the second person's opinion but now admits (or accepts openly) that the second person is right.
The second one I concede that you are right, suggests that the speaker was having an argument with the second person on something and they both held two different (probably contradictory) opinions, and now the speaker is giving up his stance, not only accepting that the second person is right but also accepting that he is wrong.
The word concede suggests that the speaker is accepting that he was on the wrong and the word admit suggests that the second person is right, it doesn't necessarily mean the speaker was wrong, it can as well mean that was the speaker always agreed with the second person but wasn't accepting it openly so far.
Both have similar use in this context.
From a tonal standpoint, though, admit sounds more personal or emotional while concede sounds calculating, like a general giving up some territory.