The 3′ and 5′ symbols refer to the order of the carbon atoms in the “backbone” deoxyribose (sugar) molecule (see lower leftbox in the image below)— numbered from 1 to 5. read more
The 5' and 3' mean "five prime" and "three prime", which indicate the carbon numbers in the DNA's sugar backbone. The 5' carbon has a phosphate group attached to it and the 3' carbon a hydroxyl (-OH) group. This asymmetry gives a DNA strand a "direction". read more
They keep talking about 3-prime (3') and 5-prime (5') Carbons. I know there's other numbers too, like 1-prime (1') and 7-prime and all this crazy stuff. Both of these numbers are at the end of a section of unwound DNA. read more