The Lord was sorry that He had made man on the earth, and He was grieved in His heart.
Some versions use the word regret instead of sorry. Regret and sorrow are both acts related to mistakes or sin. Can God be in such a position?
The Bible consistently uses human terms to describe a non-human God. Our arms are the body part that perform most of our work, so God's work is described as being done with God's "hands". Our eyes are what we use to observe and take in information, so God's observatory faculties are called "eyes". Our mouth is the body part we use to communicate, so God's words are regarded as coming out of his "mouth". Each of these body parts we understand not as literal descriptions of God, but as metaphorical - they do not apply to God in the same way they apply to humans. These are so-called "anthropomorphisms".
We must interpret "repent/relent" the same way, as an anthropomorphism. When a human repents/relents/regret, he generally speaking changes a course of action that he has previously chosen - humans tend to do this because they admit to having made a mistake and want to correct it. However, when this term is applied anthropomorphically to God, we must understand it as we understood God's "arms" and "eyes" - we must take what we know of God, and apply the term to him in a way that fits the context. In this case, I believe that "regret/relent" indicates that God has decided to discontinue a course of action upon which he has started - he will destroy most of what he has created and sustained up to this point.
Another interesting usage of such language is found in 1Sam 15:
The word for "regret" (v11) and "relent" (v29) are the same word in Hebrew. So in one sense, God can relent, and in another sense he cannot. The contexts of each of these verses makes it clear that both verses are from the human perspective: in v11, God may seem to "relent" from an action. But in v29, God is said never to "relent" from what he has spoken (that Saul and his family would not be kings). Put another way, v11 is speaking anthropomorphically, while v29 is speaking literally.
God gave us the freedom to act. That's God's principle and he cannot go against it.God always hope we will act well, but God CANNOT FORCE us to be good. God was hoping Adam and Eve would obey his commandment not to eat of the fruit of the Tree of KGE. Weather A & E eat of the fruit was not decided yet. God didn't know yet. It was entirely depending on A & E personal decision and responsibility. Unfortunately, A and E went against God's expectation and ate the fruit, causing their Fall and their descendants to carry evil nature. "God regrets he created man" means God suffers like a father whose children are misbehaving badly. He is disappointed. If the Fall was planned by God, it is very normal humans misbehave, there is no reason for God to be disappointed and to regret he created man. Same for Saul. Same for Israel in Jeremiah 8:18;9:1 Esaiah 5:4 this shows God's disappointment. God wants Israel to become the "head" not the "tail" and to choose the blessing and not the curse. It's entirely up to Israel. God cannot force Israel to choose the blessings.God is suffering because his beloved children are suffering and misbehaving. My Father in Heaven is sad, suffering, disappointed when I go astray.
As Niobius says in his answer, the use of anthropomorphisms is part of God's communication with man. It isn't necessary to imagine God's "outstretched arm" is literally flesh and blood, and you don't necessarily have to imagine God has emotions or regrets in the same sense that humans do: an anthropomorphism is an illustration in terms we can understand that reveals a degree of the reality of God.
However there is meaning behind the anthropomorphism. God may not have an arm of flesh and blood, but He can do anything a flesh and blood arm can do, and of course, much much more, with His 'arm'. Likewise, though God's emotions may not be just like ours, what He does have is surely something higher, deeper, more complex and more wonderful.
…this is incorrect on several levels:
If we insist that God is perfectly simple then the Bible is full of contradictions, but if we allow Him to be perfectly complex we can make sense of this and other verses that imply He is torn in two directions or 'changes His mind'. You might like to look at the following verses among others that might provoke similar questions: