Kaffara (expiation) for breaking an oath or vow is detailed in the Quran:
فكفارته إطعام عشرة مساكين من أوسط ما تطعمون أهليكم أو كسوتهم أو تحرير رقبة فمن لم يجد فصيام ثلاثة أيام
Its expiation is to feed ten poor persons at an average of what you feed your family with, or to clothe them, or to free a slave. However, if someone cannot afford, he has to fast for three days.
— Quran 5:89
You can choose between freeing a slave, giving clothing to ten people or feeding them. If you can genuinely not afford any of these, then you can fast for three consecutive days.
Since you've specifically asked about the nature of food given for Kaffara, I will limit my answer to that.
Note that the description of the type and quantity of the food in the Quran is:
أوسط ما تطعمون أهليكم
the average of that which you feed your [own] families
Which means that it should neither be meager nor very excessive. Rather it should be an average meal of normal quality that will sate a hungry person and which you would eat in everyday routine.
Quantity of food:
According to the Hanafis and Malikis it is adequate to feed each needy persons two meals (such as breakfast and dinner) so that they eat their fill. This is the average (أوسط) amount of meals in a day.
The same ten people must be given both meals. You can not give one meal to one person and the next meal to another person who didn't eat the first meal. This is to satisfy the minimum amount of food per person.
Alternatively you can give each person a certain quantity of staple food. According to the Hanafis this quantity is the same as the quantity of food to be donated per person in Sadqatul Fitr, i.e. half a Sa' of wheat or a Sa' of dates etc. 1 , 2 , 3 , 4
Requirements about the needy people:
They must be Muslim according to the majority of the madhabs, because Kaffara is a ritual charity and these can only be given to Muslims, similar to Zakat.
They should not be people regarding whom it obligatory on you to spend on their maintenance (such as your family or spouse).
They should not be infants or children who would eat very little.
Further References (Arabic):