Isaiah 7:20 (NASB)
In that day the Lord will shave with a razor, hired from regions beyond the Euphrates (that is, with the king of Assyria), the head and the hair of the legs; and it will also remove the beard.
This does seem like an odd verse when pulled out of its full context, but reading the entire passage in historical context and in light of the law of Moses, specifically Leviticus 14, the meaning becomes apparent.
The prophet Isaiah, in Isaiah 7, was announcing the destruction of the land of Israel by the Assyrians. The attacking hordes are compared to flies and bees (verse 18). They will enter the land and consume it (verse 19).
A picture is then presented of the shaving off of all hair on the head and body, an apparent reference to the cleansing of a leper in Leviticus 14:8-9.
Leviticus 14:8-9 (NASB)
And [the leper] that is to be cleansed shall wash his clothes, and shave off all his hair, and wash himself in water, that he may be clean: and after that he shall come into the camp, and shall tarry abroad out of his tent seven days. But it shall be on the seventh day, that he shall shave all his hair off his head and his beard and his eyebrows, even all his hair he shall shave off: and he shall wash his clothes, also he shall wash his flesh in water, and he shall be clean.
Part of the leper's cleansing involves the removal of all hair, and the nation that would be overrun by the Assyrians would be cleansed through the removal of the sinful Israelites.
The shaving is therefore a figurative picture of cleansing taken directly from Levitical law. Even without referencing the Levitical law, we see it nonetheless presents the picture of the land being wiped clean of inhabitants.
We are then, in the following verses, informed that when everything is over there will be so few people left in the land that animals will have plentiful pasture and sheep will overrun it. It will flow with milk and honey because there is no one there to consume the milk and honey or to prevent the animals from having the best pasture land available. The cultivated land will be overrun with wild growth. Vineyards will turn into thorn patches, etc, because there will be no one to tend them.
In fulfillment of this prophecy, the king of Assyria conquered the nation of Israel around 722 BC, killing and deporting huge numbers of Israelites.
2 Kings 18:9-12 (NASB)
Now in the fourth year of King Hezekiah, which was the seventh year of Hoshea son of Elah king of Israel, Shalmaneser king of Assyria came up against Samaria and besieged it. At the end of three years they captured it; in the sixth year of Hezekiah, which was the ninth year of Hoshea king of Israel, Samaria was captured. Then the king of Assyria carried Israel away into exile to Assyria, and put them in Halah and on the Habor, the river of Gozan, and in the cities of the Medes, because they did not obey the voice of the LORD their God, but transgressed His covenant, even all that Moses the servant of the LORD commanded; they would neither listen nor do it.
Ultimately, we who are called by God are cleansed through the finished work of Jesus Christ on the cross, who cleanses us from all unrighteousness (1 John 1:9). In terms of your standing with God, if you are a follower of Christ, He has fulfilled the ceremonial cleansing of the razor (Hebrews 8:6-10:10).