What is Skill in Battlefield 3?

It's an ELO-like calculation that can be used to try to make matches with opponents of roughly the same skill level. I wouldn't worry about whether it's "good" or "bad," but track changes in my own score over a period of time. A good goal is to consistently improve your score

The BF3 forums have a rough explanation of how it's calculated:

So basically, this is what determines your skill level on your stats page:

• You gain/loose[sic] SL based on every confrontation with another player
• Killing a highly skilled enemy gives you more points than killing someone less skilled
• Points are not transferred from a player to another, they are simply added/subtracted based on the encounter and the SL of both parts (thus, after an encounter, one part may go up 50 points while the other loses only 20)
• The SL is used for matchmaking

Directly from Dice:

"So basically, this is what determines your skill level on your stats page:

• You gain/lose SL based on every confrontation with another player • Killing a highly skilled enemy gives you more points than killing someone less skilled • Points are not transferred from a player to another, they are simply added/subtracted based on the encounter and the SL of both parts (thus, after an encounter, one part may go up 50 points while the other loses only 20) • The SL is used for matchmaking "

It does not say what skill is high or what is low. Each match your skill is calculated then on battlelog you get your total skill over the course of every game you have played.