When used as an adjective, it is the opposite of clarity. It is a person, or a type of communication (written, oral, digital, etc) that is vague and unclear, despite volume.
It is prose that has a great deal of complicated information, but not simplicity.

If form follows function, people who are obtuse have little or no function. (Except perhaps to annoy the rest of us).

William F. Buckley comes to mind.

Ob*tuse" (?). a. [Compar. Obtuser (); superl. Obtusest.] [L. obtusus, p.p. of obtundere to blunt: cf. F. obtus. See Obtund.]

1.

Not pointed or acute; blunt; -- applied esp. to angles greater than a right angle, or containing more than ninety degrees.

2.

Not having acute sensibility or perceptions; dull; stupid; as, obtuse senses.

Milton.

3.

Dull; deadened; as, obtuse sound.

Johnson.

 

© Webster 1913.