What are vows? Are they relevant even today? Psalms 76:11 (NIV) says 


  Make vows to the LORD your God and fulfill them. 


Many other passages in the old testament as well we hear about vows and fulfilling it.

In New testament we read in Acts 18:18 (NIV) 


  Paul stayed on in Corinth for some time. Then he left the brothers and sisters and sailed for Syria, accompanied by Priscilla and Aquila. Before he sailed, he had his hair cut off at Cenchreae because of a vow he had taken.


Also we read in Mathew 5:33-35 (NIV) we see reference of vow: 


  “Again, you have heard that it was said to the people long ago, ‘Do not break your oath, but fulfill to the Lord the vows you have made.’ But I tell you, do not swear an oath at all: either by heaven, for it is God’s throne; or by the earth, for it is his footstool; or by Jerusalem, for it is the city of the Great King.


Questions:


What are vows? 
Are they  relevant even today? 
For what, we need to make a vow? 
Why would have Paul vowed to cut his hair? 
Why we do not hear about such vows these days in churches?
Well, I suggest you read A Defense of Rash Vows by G.K. Chesterton for more enlightement.


  Modern sages offer to the lover, with an ill-flavoured grin, the largest liberties and the fullest irresponsibility; but they do not respect him as the old Church respected him; they do not write his oath upon the heavens, as the record of his highest moment. They give him every liberty except the liberty to sell his liberty, which is the only one that he wants.


But here's the gist of it.  


Married couples make a vow to each other, with Christ as their witness
Priests and others make vows to the Catholic Church or consecrate themselves to Mary (as I have).
Other vows can be of a more mundane purpose (I promise to eat my weight in kelp), but still important to keep if for no other reason than, 'to thine own self be true'



  The man who makes a vow makes an appointment with himself at some distant time or place. The danger of it is that himself should not keep the appointment. And in modern times this terror of one's self, of the weakness and mutability of one's self, has perilously increased, and is the real basis of the objection to vows of any kind. A modern man refrains from swearing to count the leaves on every third tree in Holland Walk, not because it is silly to do so (he does many sillier things), but because he has a profound conviction that before he had got to the three hundred and seventy-ninth leaf on the first tree he would be excessively tired of the subject and want to go home to tea. In other words, we fear that by that time he will be, in the common but hideously significant phrase, another man.


Making a vow gives an individual the liberty to constrain themselves.  Modernity rejects this notion because it rejects obedience (even to yourself) and it rejects truth (even being honest with yourself).  So, in the sense that no one will take your vow seriously, yes they're irrelevant today.   But to the Christian, who does not live in accord with the age, vows are very important and they can help us to be obedient to the Church and to Christ.  

Good vows will keep our wills as closely aligned to God's as possible.