Muzzle flash is the emission of light caused by burning propellant or energetic by-products leaving the muzzle of a gun, typically directly after a bullet. In most cases, this is in gaseous form, and those gases are glowing due to their temperature, emitting light.
Muzzle flash varies among weapons, between types of ammunition, even from round to round. During the day, it can usually be ignored as only in the most powerful weapons will it be able to compete with daylight. However, indoors or at night it can pose significant problems for the shooter. Not only can the flash interfere with night vision, ruining dark adaptation at what is likely a critical time, but it can also give away the position of the shooter.
There are a few means of reducing muzzle flash. Suppressors (more commonly and incorrectly known as 'silencers') attempt to trap the escaping gas, holding it long enough to slow it down and cool it. This will reduce both the noise of the shot as well as the muzzle flash, as the gas will have cooled by the time it escapes the suppressor. Flash suppressors (also known as flash hiders or flash guards) are devices attached to the end of the barrel which are concerned solely with flash and not with the sound of the shot. There are three general shapes of flash suppressor, and they perform slightly different tasks. The duckbill suppressor comprises two prongs, one above and one below the bullet path, both flattened. This has the effect of directing the gases out to the left and right as the bullet passes through the suppressor; this prevents them from moving above the barrel into the line of sight of the shooter and interfering with the shooter's vision. The birdcage suppressor looks like a duckbill model with a ring at the end, and may have more than two prongs in order to direct the gases in various directions (an 'X' shape, with the shooter's line of sight between the top two arms, is widely used). Finally, a simple cone may be used in an attempt to block the gases from the shooter's line of sight entirely. This will only be useful in weapons large enough that the shooter's sight line is displaced high enough from the barrel to avoid the cone, otherwise it will interfere with aiming.
All of these solutions aim to reduce the effect on the shooter. Some are modified to attempt to reduce the signature downrange as well; attaching 'front guard' blades to a birdcage suppressor, so that the sideways-moving gas jets are shielded on their front edge, will reduce the signature of the shot from the target area but will make the weapon more unwieldy and more likely to catch on or entangle foliage or other obstacles.