A vow is a promise or oath.
You should feed ten poor persons or give them clothes. If you can not afford that, then you must fast three day. It is called Kaffara al-Yameen.
The Qasam which is obligatory to fulfill is when you take the name of Allah in it. If you did not take the name of Allah, then such Qasam is not obligatory and no Kaffara on you if you do not fulfill it.
It is obligatory to fulfill the promise to Allah, and if you did not fulfill it, you will be committing a sinful act and there is a Kaffara on you which is either, freeing a slave, or feeding sixty poor persons or fasting two months.
We are not allowed to change our mind after promising Allah.
The Promise should be pronounced verbally and not just in your heart.