1 Samuel 16:13 - Wesley's Explanatory Notes

Anointed him — David's brethren saw David's unction, yet did not understand, that he was anointed to the kingdom; but were only told by Samuel, that he was anointed to some great service, which hereafter they should know. Thus Jesse only, and David, understood the whole business, and his brethren were able to attest to that act of Samuel's anointing him, which, with other collateral evidences, was abundantly sufficient to prove David's right to the kingdom, if need should be. The spirit, &c, — That is, he was immediately endowed with extraordinary gifts of God's Spirit, as strength, and courage, and wisdom, and other excellent qualities which fitted him for, and put him upon noble attempts.