People think that the Level2 data provides an additional clue about the direction, which the stock will probably choose to go in the short term.
The knowledge of who stands on the ladder with requests and which way the market makers are trading could bear very important for the day trader.
Level 2 quotes allow seeing most of it and the market depth for a particular stock. In other words, it's the offer, that can put pressure on the ladder's best prices, and describes the strength of a possible drop in resistance or growth stock's rates.
As a day trader, try to act as the most important market maker in a particular stock, it usually leads to greater success. Good luck!