Natural law is, in general terms, the idea that there is some sort of right and wrong that exists outside of human control and convention; a sort of "poetic justice" that transcends our power and understanding. It is contrasted with human law or common law, wherein humans ascribe a contextual and shifting definition of right and wrong.
This seems inherently contradictory; how can anything be "naturally" right or wrong? This paradox is the question that philosophers such as Aristotle addressed when dealing with this concept. Aristotle is, rightly, credited with an enormous influence on Western civilization, although he was not always correct, nor was he always interpreted correctly. Aristotle and other early philosophers approached the problem of natural law by reasoning that 1. the universe seems orderly, 2. law and order go hand in hand, and 3. we have an innate sense of right and wrong. Therefore, the universe is governed by laws; these laws are natural laws, and they are revealed to us by our conscience. Any two people, no matter their differences, will agree that acts of theft or murder are considered wrong; this is the natural law in action.
Thomas Aquinas was a 13th century Christian philosopher who agreed with many of Aristotle's positions on natural law, and expanded upon them; Aquinas is considered a figurehead of philosophy in his own right, not just an Aristotelian fanboy. In the Christian worldview, the laws of God are the ultimate determinate of right and wrong; these laws are revealed in the Bible and the teachings of Jesus Christ. Aquinas combined this with Aristotle's perspecitve by arguing that "natural law", our innate sense of right and wrong, is an aspect of "divine law", i.e. the complete truth of God's justice. All humans understand and are exposed to natural law, but divine law must be revealed through divine teachings, in order to bring human behavior more consciously in line with God's command; humans can recognize the commission of sin, but must know what sin is in order to comprehend it and choose to avoid it.
It must be acknowledged that Artistotle was not, nor could he have been, a Christian; he may best be described as a Deist. Thus, some of these differences may stem from the different religious beliefs of these figures; it may also be argued that Aquinas cherry-picked the philosophies or ideas that matched and exemplified Christian philosophy.