This is the second world in the game, there are 25 levels and most are pretty simple to complete.
You get to unlock a ton of useful new plants as you play through this world, here is the list:
Kernel-Put - Level 1
Pretty low powered long distance plant that flings corn kernels and butter at zombies
Snapdragon - Level 3
Fairly strong fire breathing plant that will damage three tiles in each of the two columns in front of this plant. Very handy especially in the earlier levels.
Spikeweed - Level 6
Destroys one rolling zombie and damages any zombies that trample on them. Not too useful, but handy if you have some spare sun to use. Especially useful in front of a wall-nut or similar.
Spring Bean - Level 9
Bounces back zombies that get too close or bounces them into water if it is nearby. Most useful on water based levels and once the zombies are in the water they ain't getting back out!
Coconut Cannon - Level 11
Pretty strong canon that will fire a coconut down a single lane. Quite pricey to use at 400 sun, I'm not a fan of this plant due to its quite slow recharge rate and expensive cost.
Threepeater - Level 14
Very useful peashooter which hits zombies in that are in the lane where the plant is as well as the one above and below. Not too powerful, but fires at a good rate and in three lanes.
Spikerock - Level 18
Like the spikeweek, just a lot stronger - and more expensive! Quite handy in later levels where you need to maximise placements.
Cherry Bomb - Level 25
Really strong bomb which blows up most zombies in an area close to where it is detonated. It will detonate as soon as it is planted.