Essential properties are properties of an object or idea that that thing must have, or it would not be that thing.
For example, an essential property of a chair might be that you can sit on it. An essential property of a triangle is that it has three sides.
Some things don't have definite (or at least simple) essential properties. For example, most of us don't know what would be an essential property of a cat.
Compare to Accidental properties.
Baffo--that depends on whether you are using traditional Analytic Philosophy or Revisionary Philosophy. Analytically, you can shoot holes in any definition of chair you might come up with, but with revisionary philosophy a hole won't hurt anything. You use whatever the most useful definition of a chair is. (You could still modify that concept of a 'chair' with 'broken', of course.)