A quantitative measure of the resistance of an object to attempts to change its velocity.   Hence mass is a measure of inertia (from the Latin vis inertia, the force of inaction.) 


Newton equated mass and "quantity of matter", which he said arises "from its density and bulk conjointly."

Gravitational Mass, which appears in the Law of gravitation (universal), has been shown to be proportional to Inertial Mass to better than one part per trillion.  [See the Eotvos experiment page in Wikipedia, much more accurately performed at the University of Washington  - Physical Review Letters 100, 041101 (2008).]  This equality is assumed by the Principle of Equivalence and is a cornerstone of Einstein's theory of General Relativity.  This theory indicates that all forms of energy have mass via the relationship E=mc2.