Compact or standard? That is the question.
The difference between these two types of road cranksets comes down to gearing. There are advantages and disadvantages to both along with obvious reasons why you should consider one or the other.
Standard cranks are often called racing cranksets because they offer the fastest common gearing (bigger chainrings are available but must be bought separately). Standard cranks have 53/39 gearing, meaning they have a 39-tooth small ring and a 53-tooth big ring. Ring is short for chainring, which is what the front gears are called that are bolted to the cranks. The bolt circle diameter (BCD) of standard cranksets is 130mm.
Compact cranks have a smaller BCD, 110mm, which allows for smaller chainrings. Compacts have a 50/34 gearing, so losing three teeth on the big ring and five teeth on the little ring compared to a standard. Compact cranksets are preferred for climbing races or for people who like to ride fast but not race. There are many people that race compacts, but for most people it's not the preferred crankset for flatter races or any with limited climbing.
Combined with a wide-range rear cassette, like an 11-28, compact cranksets offer a wider range of gearing and -- as mentioned earlier -- are really designed to maximize one's efficiency to climb or travel at lower speeds. More recently, long-caged rear derailleurs have been more common in use with compact cranksets and 11-32 cassettes, such as SRAM's WiFLi system. This wide range of gearing means a wider range of comfortable speeds and decreases the gearing overlap (when different combinations of front gearing and rear gearing have the same gearing ratio such as a 50/25 and 34/17, both of which are 2:1 gear ratios).