Experience (or abbreviated as XP) is the points you get until the next level. You can obtain experience in many ways - you can play games with players and earn it, you can go to several places to earn it such as Flum's Fountain or Club Fling, grow plants in order to attain experience and several other methods. How much experience needed to be obtained depends on what level you are - if you are a low level and just began playing Bin Weevils, you would need just under 1000 experience, whereas on a higher level like level 50, you would need several hundred thousands of experience to level up. When you do level up, you need to go to your nest, and need to earn even more experience than the previous level you were on.
Tycoons (players who have membership) can get experience easier than players who do not have membership, as they have the ability to enter several places (at Club Fling, only tycoons can pick up experience when the streamer has been filled up, and only tycoons can pick plants from Tink's Tree) which can help them with this. However, an average player can still level up fast in the same wa as tycoons.