What is Kaffarat al-Yamin?
Question

Please explain kaffarat al-yamin (the expiation for breaking a vow) in detail.
Praise be to Allah.Kaffarat al-Yamin
Kaffarat al-yamin is mentioned by Allah in the verse (interpretation of the meaning): 
“Allah will not punish you for what is unintentional in your oaths, but He will punish you for your deliberate oaths; for its expiation (a deliberate oath) feed ten Masakin (poor persons), on a scale of the average of that with which you feed your own families, or clothe them or manumit a slave. But whosoever cannot afford (that), then he should fast for three days. That is the expiation for the oaths when you have sworn. And protect your oaths (i.e. do not swear much). Thus Allah makes clear to you His Ayat (proofs, evidences, verses, lessons, signs, revelations, etc.) that you may be grateful.” [Al-Maidah 5:89] 
So the person has the choice of three things when offering the expiation for breaking an oath :  

Feeding ten poor persons with the average kind of food that he feeds his family, by giving each person half a sa’ of the usual local staple, such as rice etc. This is equivalent to approximately one-and-a-half kilograms. If rice is usually eaten with some kind of sauce then along with the rice he should give them some sauce or meat. If he gathers together ten poor people and offers them lunch or dinner, this is sufficient. 
Clothing ten poor people, which means giving each one clothing that is suitable for praying in, so for a man he would give a thobe or dishdasha or a lower garment and upper garment (izar and rida), and for a woman a concealing dress and a head cover. 
Freeing a believing slave. 

Whoever cannot do any of the above should fast for three consecutive days. 
Can you pay Kaffarat al-Yamin in cash?
The majority of scholars are of the view that it is not sufficient to pay the kaffarah in cash . 
Ibn Qudamah (may Allah have mercy on him) said: 
“It is not sufficient to offer the value of the food or clothing to be given in expiation , because Allah mentions food, so expiation cannot be offered by any other means, and because Allah has given us a choice between three things, and if it were permissible to pay the value, the choice would not be limited to these three things…” (Al-Mughni by Ibn Qudamah, 11/256) 
Shaykh Ibn Baz (may Allah have mercy on him) said: 
“But the kaffarah should be offered in the form of food , not cash, because this is what it says in the Quran and Sunnah. What must be offered is half a sa’ of the local staple food, whether it be dates, wheat or something else. That is equivalent to approximately one-and-a-half kilograms. If you give them lunch or dinner, or give them clothes which are suitable for praying in – namely a thobe or a lower and upper garment (izar and rida) – that is sufficient.” (Fatawa Islamiyyah, 3/481) 
Shaykh Ibn ‘Uthaymin said: 
“If a person cannot find a slave to free, or clothes or food to give , then he must fast three consecutive days with no break in between.” “Manar al-Islam, 3/667”
And Allah knows best.