Simply put, a Roman Consul was the highest elected official in the Republic. The idea was that two consuls were elected each year, and one would rule one month, the other the next month, alternating back and forth throughout the year. One also had veto power over the other in order to encourage more fair rule. The office changed once the Republic was destroyed and the Empire rose after which it really became nothing more than a figure-head type position.
Originally the consuls were referred to as praetors, because most of the officers were leaders in the military who then took on the jobs of civilian rule. The consuls were almost always elected from aristocratic families, though there were thought to be rare exceptions to this rule once the laws were changed to allow plebeians to stand for the office around 360 BC.