DNA and RNA are structurally almost identical, but there are a number of key differences. The 'D' in DNA stands for deoxyribose - the sugar molecule that gives DNA a stable helical conformation (called a B-helix). Contrastingly, the backbone in RNA is ribose - the 'R'. Ribose possesses an extra hydroxyl (-OH) group, creating a different helical structure in RNA (called an A-helix, and it is often single stranded). Additionally, the four bases of DNA are adenine, cytosine, guanine and thymine, whereas in RNA, thymine is substituted for uracil, which still pairs with adenine.
While both molecules are used to store information, they are structurally different. This makes them functionally different too. RNA is less stable, as the extra -OH group interferes with the stable helical conformation and is generally more reactive, occurring mainly as a single-stranded molecule. As it is less stable, it is used for relatively short term transfer of genetic information, and is constantly being used and recycled in the cell - examples being messenger RNA (mRNA) and transfer RNA (tRNA). Compare this to DNA - it is more stable, so it is used for long-term storage of genetic information, and is kept as tightly packed, inaccessible coils deep in the cell's nucleus.