A good definition for irrational: 1) Rigid, 2) inconsistent with reality 3) illogical 4) interferes with your psychological well-being and gets in the way of pursuing your personally meaningful goals.
Irrationality is the reaching of a decision or conclusion that is not the best decision or conclusion that could have been reached in the light of the evidence, given the time constraints that apply.
As used in this definition, "best decision" means the decision that is most likely to achieve the result desired by the decision maker. "Best conclusion" means the conclusion most likely to be "correct" within the reasoner's frame of reference.
The Notorius Five
There are five irrational beliefs that many of us hold and that we can learn to un-learn.
The Notorious Five are:
1. Musterbation (shoulding, demandingness). I must succeed and obtain approval.
2. Awfulizing. I lapsed two weeks ago. Isn't that just awful? [No.]
3. Low Frustration Tolerance. I can't quit smoking; it would be too hard for me. [Cancer is even harder.]
4. Rating and Blaming. I'm worthless because I made a mistake, or, the world's a rotten place to live. [Know a better one?]
5. Overgeneralizing. Always or Never attitudes. AA is good for everybody; it worked for me; or, AA is a lousy outfit; I tried it and it didn't work for me."