"I take your point" is not a native English phrase in the US. Agreeing and understanding are two different things. Agreeing phrases commonly used in the US: "I agree." "Agreed." "I agree with you." "You and I are on the same sheet of music." "Exactly." "I hear you." Understanding phrases commonly used in the US: "Understood." "I understand." "I understand your point." "I hear what you are saying." "Makes sense". None of these phrases indicate you agree - only that you understand. Accepting someone's point of view means that you accept that they have their own point of view - whether it is similar to yours or not - and that you aren't angry with them about it. You are ok that they have their point of view. Hope that was helpful. :)

I understand it to mean “I understand your argument”, but according to Wiktionary ( https://en.wiktionary.org/wiki/take_the_point#English ) it can also mean to agree with your point of view. I suggest you ask if in doubt. I think people will quite often say “I take your point, BUT I think that...” If they just say “I take you point” and nothing else, you’d better ask if that means they agree.