"Allah will not take you to task for oaths which you may have uttered without thought, but He will take you to task for oaths which you have sworn in earnest. Thus, the breaking of an oath must be atoned for by feeding ten needy persons with more or less the same food as you are wont to give to your own families, or by clothing them, or by freeing a human being from bondage; and he who has not the wherewithal shall fast for three days [instead]. This shall be the atonement for your oaths whenever you have sworn [and broken them]. But be mindful of your oaths!' Thus Allah makes clear unto you His messages, so that you might have cause to be grateful." (Qur'an:5:89).
Based on this, if someone makes a solemn oath and breaks it, he or she is obligated to expiate for it by feeding ten poor people or clothing them; if someone cannot do so, he or she should fast three days by way of expiation.
The Prophet (peace be upon him) said, "Whoever makes an oath to do something, but later finds it, a better option, let him do the latter and expiate for his oath" (Reported by Muslim).
Coming to specifically to feeding the poor, the scholars are of the view, originally it was estimated to be providing a mudd of any staple foods of a country; and a mudd is estimated to be a little more than half a kilogram by today's measurements. The preferred view of many scholars is, one may fulfill the requirement by providing for two main meals of the day (i.e. breakfast and dinner). It should be given to ten poor people; however, some say, if one gives it to a single large family that would be fine as well. This is based on an inference from a tradition in which the Prophet (peace be upon him) ordered the poor man- who had broken his fast in Ramadhan through deliberate sexual intercourse- to feed his family.
Based on this, you should preferably give it to ten poor persons; otherwise you may give it to a single large family. If, however, you wish to give to more than ten people, you may do well to increase the amount, accordingly, to be on the safe side. It is always good, in such cases, to err on the side of giving rather than withholding.