Historically speaking, an overseer was employed on a plantation to keep slaves in line. He worked for the plantation owner, but whereas the plantation owner would not get his "hands dirty," considered a "gentleman," the overseer would make sure work was done and peace was maintained, and would dole out punishment as needed.
Punishment could be administered by the plantation owner..., and most often by the overseer or driver. Slaves were punished with a variety of objects and instruments. Some of these included: whips...Those who punished slaves also used weapons such as knives, guns, field tools...The whip was the most common instrument used against a slave.
It was not unusual that an overseer would use a whip, and though it could cause a great deal of physical damage, it could also kill someone if he/she were beaten badly. Many plantation owners believed that fear and terror were the only ways to motivate slaves to work, and they used overseers to see this taken care of.
The presence and "responsibilities" of overseers is recorded in slavery literature:
Thinly veiled acts of miscegenation and heroic escapes from sadistic overseers appear in most slave narratives, along with the primary antislavery message.
Some overseers, ironically, whipped slaves while they quoted scriptures from the Bible, somehow maintaining (in their minds) that slavery and beatings were condoned by God.
Slave narratives detail whippings by "Christian" overseers that are accompanied by recitations of scripture. The biblical justification of slavery becomes the single most important rhetorical argument upholding the bondage of an entire race.
I assume that you are asking this question in the context of slavery. If so, the overseer was an employee of the plantation owner. This person was a sort of manager who helped the owner run a plantation. Typically, this person was hired from among the white people living in the area around the plantation (as opposed to being from the master's family).
Overseers had a reputation for being fairly brutal. They were often the ones responsible for punishing the slaves who broke rules or failed to work well enough. They were typically said to have less incentive to try to be at all humane to the slaves because it was not their money that bought the slaves. As the link below says (at least on plantations where the owner was not present):
... overseers were notorious for their abuse of power and their violence against slaves.
Needless to say, there were variations among individual overseers.
The brief answer, then, is that an overseer was a white man hired by a plantation owner to be something of a manager for a large plantation.