Obvious answer, they're meant to be the prototypical Men in Black which UFO folklore has covering up incidents by altering the scene and eliminating witnesses. Why black suits? They're associated with government figures due to a combination of formality requiring regular wearing of suits and low wages meaning that a government employee only owns so many suits — dark suits don't show stains as badly, so you can wear them more days in a row. Therefore, government agents, or beings want to look like government agents, would show up in a dark suit. In addition, you have the association of black with mourning clothing, which means that this monochromatic sartorial styling adds an association of death and lack of humor to the agents.
As to why the MiB of the movie universe haven't moved on to something less conspicuous, for one, the legends of dark-suited men coming around for strange happenings simply provides a standard uniform. People are likely to listen to someone who looks suitably governmental. Lastly, it provides a standard uniform for the group, providing a sense of unity and belonging, and I can vouch from experience that governments take a long time to change their stylings.
From a practical standpoint, suits make for lousy field clothing — they tend to be hot and restrictive, and the risk of damage in the field means you'd generally prefer to be wearing something else if you face combat. But in the context of supertechnology, a full suit makes sense because it covers much of the body, allowing you to hide armor, and typically includes many pockets, allowing you to hide more gadgets. The usual liabilities of heat and restriction are dealt with by futuristic materials.