Genèse 4:15

And the Lord said to him, Behold now, any one who killeth Kain, unto seven generations vengeance shall be taken of him. And the Lord sealed upon the face of Kain the mark of the Name great and honourable, that any one who might find him should not kill him when he saw it upon him.

Now because Scripture says, And the Eternal appointed a sign for Cain, and it does not say, “and G-d gave him a sign,” or “made him a sign,” it indicates that He appointed for him a steady sign which would always be with him. Perhaps it indicates that as he wandered from place to place he had a sign from G-d indicating the way in which he should walk, and by that he knew that no misfortune would overtake him on that road.
In Bereshith Rabbah the Rabbis similarly stated, “Rabbi Aba said: ‘He gave him a dog.’” Since he feared the beasts, He gave him one of them to walk before him, and wherever the dog turned to go, Cain knew that G-d commanded him to go there and that he would not be killed by any living creature. Now the Sages singled out a contemptible sign [a dog] as was befitting him, but the intent is that there was with him a perpetual sign showing him the way to go for such is indicated in the word vayasem (and He appointed).

כל הורג קין שבעתים יוקם, I, G’d, announce that anyone who dares to kill Kayin, [i.e. who takes the law into his own hands, Ed.] would be punished seven more times than what the crime he committed appears to warrant. Anyone who is prepared to kill someone is called הורג, as for instance, in Hoseah 9,13 ואפרים להוציא אל הורג בניו, “Ephrayim too must bring out his children to his slayers.” The word שבעתים means “twice seven times,” as in Proverbs 6,31 ונמצא ישלם שבעתים, “when he is found out he must pay twice sevenfold.” G’d decreed therefore that when someone killed half the human race, or at least a third of the human race, the appropriate vengeance would involve a twice sevenfold penalty. This would manifest itself in such a slayer being a restless wanderer on earth for seven generations. Such a life is considered worse than death. When David prays in Psalms 59,12אל תהרגם פן ישכחו עמי הניעמו בחילך, “do not kill them lest my people will forget them; make them wanderers seeing it is in Your power,” he meant that they be killed only at the end of seven generations. David wanted the punishment of his enemies to last. If they would all die and disappear at once their absence would soon be forgotten. Kayin got his deserts at the end of seven generations as we know from traditional sources in Tanchuma 10.

ויאמר לו ה' לכן כל הורג קין שבעתים יוקם, I have decreed that anyone killing Kayin will be punished twice sevenfold for that deed, irrespective of whether the killer is man or beast. The number “seven” mentioned here is not to be understood literally, but is a figure of speech for multiples of one. The number is used in a similar sense in Leviticus 26,21 where it also does not mean that G’d will punish the Jewish people sevenfold for each of their sins, but He warns them that their punishment will be very severe. In Proverbs 24,16 שבע יפול הצדיק וקם, the meaning is also not that the righteous will fall down seven times and rise again, but that even if a righteous person falls on bad times repeatedly, being righteous, he will recover. These many ways in which a killer of Kayin would be avenged could be that his killer will be afflicted with numerous sicknesses, diseases, not with just one. They would afflict him successively, until he will succumb to the last such disease.
According to Torah Shleymah on our chapter item #114 G’d told Kayin that in consideration of the fact that he now displayed fear of and reverence for G’d, he would have his lifespan extended for seven generations. Onkelos explains the expression שבעתים as receiving punishment spread over seven generations. Just as Kayin’s eventual death was suspended for 7 generations, so he who killed him would experience a similar fate. Eventually, Lemech killed Kayin. He was the sixth generation after Kayin, but the seventh counting from Adam.

וישם ה' לקין אות, He gave him a sign in his heart, i.e. He fortified his self-confidence which had been shattered. G’d made the various beasts and men who would be born after him be in awe of him so that they would not attack him. We will come back to allegorical material pertaining to this verse when we explain verse 23.

לכן כל הורג קין שבעתים יוקם, “therefore whosoever slays Kayin, vengeance will be taken on him sevenfold.” The plain meaning of this verse is that seeing that Kayin was worried about being murdered, G–d assured him that anyone murdering Kayin even after he had lived seven generations would be held accountable by Him. This is why Lemech who held himself as guilty of killing Kayin, even though he did so unintentionally, told his wives what would happen to anyone killing him on that account (Compare verse 25 in this chapter.) Lemech’s children were the seventh generation, after Adam. (Adam-Kayin-Chanoch-Irod-M’chuyael-M’tushael-Lemech-(Yaval,Yuval Tuval Kayin) He told his wives that the whole generation of such a killer fathered by himself would be held responsible for his murder by G–d, seeing that what he had done was due to his being blind and therefore totally innocent of any intent to harm a human being.