1. It is completely possible to have over 50 creeps while your enemy has less than 10 by zoning them out of experience / gold range.
2. You can bait enemies into your mushrooms and kill them, making them insanely angry.
3. You can steal buffs very quickly with your high damage from Blinding Dart (Q), Toxic Shot (E), and Noxious Trap (R) before the enemy jungler notices.
4. If you get in a pinch, you can hide in a bush and wait for a couple seconds to proc your passive, and the enemy team will have no idea where you went.
5. You can spam taunt and joke to make your opponents irritated and make them play worse

Pros:
Insane damage from levels 1~5 in lane
High mobility
Mushrooms can act as wards\damage\slow
Has a blind

Cons:
Short attack range
very weak outside of laning phase
Does almost nothing in team fights - you want to avoid them and just split push entire game

The counters of Teemo are:
Skarner
Jayce
Shen

Toxic Shot:
Teemo's basic attacks poison their target, dealing 10/20/30/40/50 (+0.3*AP) magical damage upon impact and 6/12/18/24/30 (+0.1*AP) magical damage each second for 4 seconds.
Cost
30/35/40/45/50
Range
0
Cooldown
8/8/8/8/8 Seconds
And
Noxious Trap:
Teemo's basic attacks poison their target, dealing 10/20/30/40/50 (+0.3*AP) magical damage upon impact and 6/12/18/24/30 (+0.1*AP) magical damage each second for 4 seconds.
Cost
30/35/40/45/50
Range
0
Cooldown
8/8/8/8/8 Seconds