Each nucleic acid has a 5-carbon (pentose) sugar as a part of its polymer backbone. For DNA this sugar is deoxyribose, while for RNA it's ribose:
Notice the numbering convention here. For now, since there are no attachments to these sugars, the carbons are numbered 1 through 5. Later, when we attach the base, the sugar carbon numbers will change to 1' through 5'.
The difference between ribose and deoxyribose is the presence of the OH on the 2 (2') position. DNA is 2'-deoxy. This is critical to understanding the chemistry of these two polymers.
Because of this difference, RNA is an inherently less stable molecule than DNA. For instance, RNA can readily be hydrolyzed at high pH (> 8.0). The reaction involves the 2' OH group of the polymer.