At the technique level there are two main types of man coverage, press and off. Press man is where a corner will line up inside and very close to the wide receiver at the line of scrimmage. The goal is to disrupt the receivers ability to run a route by hitting him repeatedly in the five yards after the line of scrimmage, if the receiver is able to get into a route the corner is betting that he is able to keep pace with the receiver until the quarterback is sacked or forced to make a bad throw. The drawback is that if the receiver can get past the defender the defender is reliant on being fast enough to catch up. That’s usually not a good look for the defense.
The alternative is off man, wherein the defender will line up about 7 yards from the line of scrimmage. The defense is ceding a clean release into a route in exchange for a decreased risk of having a receiver beat them deep. Linebackers, particularly inside linebackers, almost exclusively play this sort of coverage since they are matched up on running backs. If the backs stay home to block the linebackers are free to either blitz or "play football" and try to read the QB to break up passing plays.
Both varieties of man coverage have a few weaknesses. One is that if the quarterback decides to scramble five defenders will have their backs turned, and often the quarterback will see a lot of open grass in front of him. In addition crossing routes at the line of scrimmage can often serve to "pick" a defender, with the receiver springing free. Mesh and switch concepts are good examples of this. In addition if the offense finds a matchup it can exploit the defense often has very little it can do. If the defense is at an athleticism disadvantage then, well, you’re sort of screwed. But that tends to remain true regardless of scheme.
Within the various man schemes there are a handful of (main, at a more specific level there are tons of tiny variations) schemes defenses will use. The most conservative of these involves two deep safeties. The safeties will split the field, each covering a half of it, and provide deep coverage support on any routes being run on their side. This helps provide more insurance that the defense will not be beat over the top as well as minimizing the risk a receiver can make one defender miss and things turn into a footrace. The downside is that in this variety of man coverage the defense cannot have more than four pass rushers.
The next variety of man coverage is known as cover one. In cover one there will be one deep safety, usually the free safety, playing at least a dozen yards from the line of scrimmage and trying to read the quarterback so as to be able to break up any deep passes. This frees up one more defender to perform a variety of tasks. Sometimes this extra player (sometimes the strong safety, sometimes a middle linebacker, depending on who the defense wants in man coverage) will help another defender with a dangerous receiver by double teaming him. Sometimes this extra defender will become a fifth pass rusher. Sometimes he will spy the quarterback. In "robber" variations of cover one this extra defender will take a zone and try to help cover any short to intermediate crossing routes.
The final, and most aggressive variety of man coverage, is known as cover zero. In cover zero there is no deep safety help. There are five men covering the offenses five receivers, and the other six are free to do what they please. Almost always this means rushing the passer. This is an all out blitz, either the defense gets pressure quickly and forces a bad pass or a sack or the quarterback will have time to wait for one receiver to beat one defender. This is one of, if not the most, high risk high reward calls a defense can make. Sometimes the defense will even rush seven, with the two outermost pass rushers serving as peel rushers. Peel rushers are rushing the quarterback, however, if a running back releases into a route they will peel off to cover the route instead of blitz. Usually teams use linebackers for this, however it is not unheard of for defensive ends to play this role.
Man coverage presents teams a lot of potential choices, with the various iterations able to provide answers for most things a defense faces. For teams with superior athleticism man coverage allows their defensive backfield to blanket the opposing receivers and snuff out the life of the offense. Like any scheme man coverage is great if you have the players to run it.