The Lord spoke to this fearful king--please note that the threat he fears is real, that's he's not just timid. "Ask me for a sign," the Lord said. But Ahaz refused saying "I will not test the Lord." We can interpret his refusal as piousness or as an unwillingness to know what God wants him to do after he has already decided what's best.
The Lord gives him a sign anyway.
Ahaz had been focusing on kings and armies and enemies. Isaiah points his attention to a young woman who is about to bear a child, "She will name him Immanuel, God is with us. What you fear, you need no longer fear."