Oh, man.  There are so many definitions for this word.  Here we go…

 1. Sharp at the end.  An acute angle in geometry, is one which is less than a right angle, or less than ninety degrees. An acute angled triangle is one whose three angles are all acute, less than ninety degrees each.

2. When the word is applied to mental powers, it means: penetrating;

discerning; quick witted, as an acute reasoner.

3. Quick sensibility; having power to feel or perceive small objects; as, a man of acute eyesight, hearing, or feeling.

4. An acute disease, is one with violent symptoms, opposed to chronic.

6. In music, acute is applied to a tone which is sharp, or high; opposed to grave.

7. In botany, ending in an acute angle, as a leaf or perianth.

Acute comes from the Latin verb acuo, acuere, acui, acutus, meaning: to sharpen.