Availeth
means,


Succeeds, benefits, accomplishes.
Having the necessary force, ability, or strength to accomplish
the desired goal. 
And the prayer of faith shall save the sick,
and the Lord shall raise him up;
and if he hath committed sins,
they shall be forgiven him.
Confess your faults one to another,
and pray one for another, that ye may be healed. 
The effectual fervent prayer   
of a righteous man    
availeth
much.   

James 5     
15-16