Dividing, death, pain, strength, and strenuous labors. Strength of character. Strength, perseverance. An axe is generally associated with destruction. We use it to break things up, and in popular horror movies it is used to kill people. The ax can also be used to carve and create art, furniture or other tools.
If your dream was violent, then you may be experiencing frustration, anger and hostility.
If there was no violence in your dream, then the ax may be positively interpreted as a symbol of productivity and creativity. Either way, an ax is a powerful tool, and as a dream symbol it may be saying something about your personal power and its expression.