APR (Annual percentage rate) refers to the nominal interest rate the bank tells you it will give you for that year. For e.g. 12% per annum.
However, most banks do not charge interests annually, they in fact charge interest monthly. Hence you actually do not gain 12% of interest if you put in $100 at the beginning of the year. You will get more than that. If I did this manually by month at the end of the year, my $100 will be worth $100 x (1 + 0.12/12)^12 = 112. 68. So my real interest is actually 12.68% and not 12% like the bank said.
The 12.68% is the EAR (effective annual rate). SO basically EAR is converting APR into the real interest rate and not the nominal rate. Hope that makes sense
well it doesnt necessarily only applies to banks but I used banks as it is the most common example people use.