What is the significance of saying Insha-Allah (God Willing)? Is uttering it considered a vow?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

According to the majority of the Hanafi, Shafi'i and Hanbali scholars, saying this phrase "Insha’ Allah" along with a vow entails that to carry out that vow is not an obligation in case the intention was to make the accomplishment of that vow contingent upon the will of Allah. Saying it with an oath does not entail commitment to accomplish that oath either, according to the four schools of jurisprudence. This is also the opinion of the majority of scholars if what is meant by uttering it is to absolve oneself from the oath, provided that the exception (phrase) is directly connected to the oath. As-Sarkhasi, a Hanafi scholar, says in ‘Al-Mabsoot’: “In our opinion, if someone makes an oath or a vow and directly says (Inshaa’ Allah), then he is absolved. In 'Al-Fawaakih Ad-Dawaani', An-Nafraawi, one of the Maaliki scholars said: “If someone said, 'I swear by Allah that if I do so and so I will be indebted a vow (as a due recompense), and says with no interval 'Inshaa’ Allah' (or any phrase that entails basing one's decisions on the will of Allah) and he did that thing, then he is free from his oath. This is concerning the unidentified (unnamed) vow. As for the identified (named) vow, no exception is valid. What is meant by "unidentified" is that the person who makes the vow says, for example, "If I do so and so, then I will be indebted a vow (without determining what this vow will be). The identified (named) vow, on the other hand, is when someone determines and names the nature of the vow to be indebted, such as fasting some days (other than the days of Ramadan), performing Hajj (Pilgrimage), Umrah, or giving charity, etc. Ash-Shirbeeni, a Shaafi'i scholar, said in 'Tuhfat-ul-Muhtaj: “If the vower relates his vow to the Will of Allah or the will of so and so (somebody else), then this vow is invalid even if that person willed, for it is not allowed to associate anybody or anything to Allah's will.” In 'Kashshaaf Al-Qinaa'; Al-Bahouty, a Hanbali scholar, said: “Exception is valid in every atonable oath such as swearing by Allah Almighty, Thihar [considering one’s wife as (prohibited to him in marriage) just as his mother is] and vows, for exception is contrary to decisiveness, and decisiveness is unfit with vows. Allah Says at the tongue of Moses (what means): {[Moses] said, "You will find me, if Allah wills, patient, and I will not disobey you in [any] order."} [Quran 18:69] Yet, Moses did not prove patience with Al-Khidr, the pious man he accompanied on a journey. Nevertheless, Allah did not punish him because he made an exception in his promise (to be patient) by saying: “Inshaa’ Allah (if Allah wills).”

Allah knows best.