While Dwarves far excel humans in feats of sophisticated invention, they do not possess the raw brutality to create inventions of mass destruction. Humans, by contrast, excel at it.
Musketeers wield the devastating human invention, the musket. These handheld cannons, while not very accurate, are powerful enough to pierce even a Dragon's scaly hide with their heavy metal shots. Musketeers are not masters of hand-to-hand combat, instead trusting in their ability to reload quickly.
Musketeers are a situational investment that don't always do very well on their own but can be an effective supplement to an army of Cavaliers or other strong melee units. They are the only race-specific Level 3 unit besides the Dwarven Balloon to not have the strike ability, putting them at a unique disadvantage against other high-level units.
Possibly the best use for Musketeers is defense of a city, since their long range and powerful shot (5 Attack and 7 Damage) can pick off even most cavalry units in a single hit. Keeping them behind your city walls and protecting them with melee units is key, since the Musketeers are helpless in close quarters. Fighting with them in an open area with no walls for cover is dangerous, since enemy units can approach more easily.
Although they can deal a lot of damage, their accuracy leaves something to be desired and they will have trouble hitting units with high Defense. Nearly any unit that manages to successfully close the gap with a Musketeer will have no problem dispatching it. With only 2 Defense, 5 Health and no ability to fight back, a Musketeer becomes just another cheap archer when under attack.
The usefulness of Musketeers in general is questionable at best. Two archers would cost less initially and the same as one Musketeer to upkeep, and they would produce faster from a Level 3 city. That would also provide 4 ranged attacks per turn (since archery attacks twice) for a total potential 8 damage and more chances of at least some damage, versus just one attack from the Musketeer which could miss. Even Ballistas can fill the role of the Musketeer quite well with the same range and a two-piece attack which can end up dealing more damage if both hits connect.