Ballet is probably the most important type of dance. It involves positions and steps that you use in just about every other type of dance. 

Jazz involves dancing to upbeat music. The dancing is usually fast also.

Tap involves dancing using your feet. The shoes you use have taps on the bottom to make noise. 

Hip-hop is a version of jazz that involves using music that is more upbeat than the music you use in jazz.

Musical theater is combination of dancing, singing, and acting. It involves doing performances from various musicals.

Lyrical is a combination of jazz and ballet mixed together. The music that is involved is usually slow.