Reggae is a music genre first developed in Jamaica in the late 1960s. While sometimes used in a broader sense to refer to most types of Jamaican music, the term reggae more properly denotes a particular music style that originated following on the development of ska and rocksteady. Reggae is based on a rhythmic style characterized by accents on the off-beat, known as the skank. Reggae is normally slower than both ska and rocksteady. Reggae usually accents the second and fourth beat in each bar, with the rhythm guitar also either emphasizing the third beat or holding the chord on the second beat until the fourth is played.
Dub is a genre of music which grew out of reggae music in the 1960s, and is commonly considered a subgenre, though it has developed to extend beyond the scope of reggae. Music in this genre consists predominantly of instrumental remixes of existing recordings and is achieved by significantly manipulating and reshaping the recordings, usually by removing the vocals from an existing music piece, emphasizing the drum and bass parts (this stripped down track is sometimes referred to as a 'riddim'). Other techniques include dynamically adding extensive echo, reverb, panoramic delay, techno beats and occasional dubbing of vocal or instrumental snippets from the original version or other works.
See Wikipedia for more information on reggae and dub music.