An avail means to use or take advantage of something that can help you. It's also possible to say that you make something available for someone else.
When we talk about availing ourselves of a service or an opportunity, it usually means we're taking what's being offered and making good use of it. For example, if there's a special sale at the store where you need to buy some things, you can avail yourself of those discounts by shopping during that time.
How common is "avail"?
Word avail is considered rare in modern English. It has a balanced usage among all categories: speech, fiction, newspapers and academic texts.
Definitions
noun
Effect in achieving a goal or aim; purpose, use (now usually in negative constructions).
Example: I tried fixing it, to no avail. Labor, without economy, is of little avail.
Proceeds; profits from business transactions.
An advertising slot or package.
A press avail.
Example: While holding an avail yesterday, the candidate lashed out at critics.
Non-binding notice of availability for work.
A readily available stock of oil.
Benefit; value, profit; advantage toward success.
Effort; striving.
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verb
To turn to the advantage of.
Example: I availed myself of the opportunity.
To be of service to.
Example: Artifices will not avail the sinner in the day of judgment.
To promote; to assist.
To be of use or advantage; to answer or serve the purpose; to have strength, force, or efficacy sufficient to accomplish the object.
Example: Medicines will not avail to halt the disease.