An excellent overview of dynamics marks can be found in the book Band Expressions (link).
A good introductory video on dynamics (link).
fff = fortississimo = loudest
ff = fortissimo = louder
f = forte = loud, full stroke ~5 inches, center
mf = mezzo forte = medium loud, center
mp = mezzo piano = medium soft, off the center
p = piano = soft, strike at ~2 inches off the center
pp = pianissimo = softer
ppp = pianississimo = softest
One of the main ways to control dynamics with a drumset is adjusting the stick height when striking a drum / cymbal. Another way to increase the volume would be to use the stick shoulder to hit the drum/cymbal.