The meaning of Oath in the Bible
(From Easton's Bible Dictionary)

a solemn appeal to God, permitted on fitting occasions (Deuteronomy 6:13; Jeremiah 4:2), in various forms (Genesis 16:5; 2Sam 12:5; Ruth 1:17; Hosea 4:15; Romans 1:9), and taken in different ways (Genesis 14:22; 24:2; 2Chr 6:22). God is represented as taking an oath (Hebrews 6:16-18), so also Christ (Matthew 26:64), and Paul (Romans 9:1; Galatians 1:20; Phil 1:8). The precept, "Swear not at all," refers probably to ordinary conversation between man and man (Matthew 5:34,37). But if the words are taken as referring to oaths, then their intention may have been to show "that the proper state of Christians is to require no oaths; that when evil is expelled from among them every yea and nay will be as decisive as an oath, every promise as binding as a vow."

See more on the meaning of Oath in the Bible:
Oath {International Standard Bible Encyclopedia}

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