(Hope I'm doing this right. Moving this from
here. I've also edited it and added to it.)
"Articulations" are appropriately named. To articulate something is to add clarity or to make something clear. These markings, found above or below a written note, specify
how to play a specific note or passage. Articulations tell us three things: 1) How to start the note. 2) The weight of the note. 3) (sometimes) How to end the note.
With this said, articulations have NOTHING to do with
note lengths or
dynamics. For example, a quarter note will last twice as long as an eighth note. A quarter note with the staccato marking does not equal an eighth note. Those are two different things that are written two different ways that mean two different things. If you want a shorter note, use a shorter note value. If you want a louder/softer note, use a dynamic mark.

Below are the specific jobs for articulations.
Staccatissimo - a very light weight note with a lifted release (also described as detached from the next note).
Staccato - a light weight note with a slightly lifted release (also described as detached from the next note).
Tenuto - a defined start, weighted note with no lift, touches the following note or rest.
Accent - a firm start, heavy weighted note with no lift, touches the following note or rest.
Marcato - a very hard start, heavier weight than an accent, sometimes played with a slightly lifted release.
The above information pertains to these symbols' origins in classical, or more "legit" playing styles, and should be consulted first when choosing appropriate markings for your music.
HOWEVERIn
Jazz styles these symbols have a different set of meanings that conflict with the above information. In jazz instrumentalists often imitate the human voice, and as such the articulation markings have been in a sense slightly redefined. In these styles they are as follows:
Staccatissimo - virtually nonexistent in jazz, but would mean really short.
Staccato - short.
Tenuto - long.
Accent - stressed with a firm start. Also often long.
Marcato - Three words: fat, hard, short. Often articulated as DAHT or BAHP.
While these definitions aren't completely true to their original meanings, they hold significance in these styles of music.