And this person will claim me on their 2020 tax return. what does this mean?

If you are referring to the question on your tax return "Can someone else claim me as a dependent on their tax return?", that question is there to identify taxpayers who made income and therefore are filing a tax return, but are still considered dependent on someone else's return, usually a parent's.  

Usually a dependent's income is so low that they do not have to file a return, but will file a return to claim any refunds of taxes withheld during the year.  The parent can still get the tax advantage of claiming a dependent that they actually still support.

Being a dependent on someone else's 2020 tax return disqualifies the person from receiving the Recovery Rebate Credit on their 2020 tax return.  

Here is a link with more information on the Recovery Rebate Credit.