I've read the term 'electron valences' in A Short History Of Nearly Everything, but it didn't actually go into what they are. I also had a friend mention 'valence electrons' to me in a conversation, but I didn't ask what they were (due to pride on my part I'm afraid. She goes to school in a different country, and I didn't want to admit her science lessons were better than mine).
So basically, what are they?