A clean boost pedal is designed to deliver uncolored, “transparent” gain, much like a microphone preamplifier. These are perfect for situations in which you want to hit the front end of your guitar amplifier harder than your pickup can naturally. Hitting your amp’s front end hard is a popular way to get “more” of whatever you like most about your amp’s sound. Clean boosts are also useful when you just want to raise the volume temporarily for a guitar solo or melody line you wish to emphasize.
Dirty boosts add their own coloration to the signal. They don’t need to be overdrive pedals, some like the Earthquaker Devices Bows are modern takes on the classic treble booster, which offers a fair amount of gain and also a notch in the high-mids. They also can be used to hit the front end of your amp harder than your guitar alone, but they definitely add their own color. Dirty boosts are very often used as “always on” pedals that contribute to the overall tone.
So if you’re looking for a way to hit your amp hard without coloring your tone, or a way to temporarily raise your guitar’s volume, a clean boost is exactly what you need. However, if you want an “always-on” boost, or a boost that will add a particular color to your tone, a dirty boost is what you want.