The Quran

لا يُؤاخِذُكُمُ اللَّهُ بِاللَّغوِ في أَيمانِكُم وَلٰكِن يُؤاخِذُكُم بِما عَقَّدتُمُ الأَيمانَ ۖ فَكَفّارَتُهُ إِطعامُ عَشَرَةِ مَساكينَ مِن أَوسَطِ ما تُطعِمونَ أَهليكُم أَو كِسوَتُهُم أَو تَحريرُ رَقَبَةٍ ۖ فَمَن لَم يَجِد فَصِيامُ ثَلاثَةِ أَيّامٍ ۚ ذٰلِكَ كَفّارَةُ أَيمانِكُم إِذا حَلَفتُم ۚ وَاحفَظوا أَيمانَكُم ۚ كَذٰلِكَ يُبَيِّنُ اللَّهُ لَكُم آياتِهِ لَعَلَّكُم تَشكُرونَ

Muhammad Asad

GOD will not take you to task for oaths which you may have uttered without thought,¹ 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 by² feeding ten needy persons with more or less the same food as you are wont to give to your own families,³ 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!⁴ Thus God makes clear unto you His messages, so that you might have cause to be grateful.

Lit., "for a thoughtless word (laghw) in your oaths". This refers primarily to oaths aiming at denying to oneself something which the Law of Islam does not prohibit (i.e.. "the good things of life"); and, generally, to all oaths uttered without premeditation, e.g., under the influence of anger (cf. 2:224-225; also 38:44 and the corresponding note 41).
Lit., "its atonement shall be" - the pronoun referring to the (implied) sin of breaking an oath. It is obvious from the context that this possibility of atonement relates only to "oaths uttered without thought", and not to deliberate undertakings affecting other persons which-as has been explicitly stated in the opening sentence of this surah - a believer is bound to observe faithfully to the best of his ability. Regarding exceptions from this general rule, see surah 2, note 212.
Lit., "the average of what you feed your families with".
Le., "do not make them lightly or often" (Razi).