I read cyclists talking about power output in watt. By knowing the figures, how does it help us to cycle better or more efficiently?
It doesn't.
At least, not if you are looking at others' figures. Essentially it is like comparing a TV against another TV.
If you have a 30" TV and you look at the ratings for a 20" TV, and they are the same; the 30" TV is more efficient (as more surface area, yet same power output hence something is better).
Likewise, on a bike, it is only really useful when compared against your own data as only you know the entire situation.
You could have a power output of 180W - but if you have a heavy bike, and have a lot of drag - that is not going to get you up to very high speeds. Conversely, a power output of only 100W, on a lighter bike with a more aerodynamic style, will give you a comparatively greater speed.
It is only really useful when comparing the data individually.
A road racer could give out 150W averagely, which would (in theory) be very efficient and optimum. But if that is the best they can output, on a MTB, that will be a lot worse speed wise due to the associated losses.
If you know your figures, then it will be useful. For example, if you know you have an average output of 100W and want to reach 120W, then there is a lot you can do to try and improve.
Ultimately, though, you merely want your power output to be greater than your power 'input' as it were, otherwise, you would not move. Personally, I do not worry about it - but to some athletes etc. it is a very important thing.
After-all greater power output generally means greater speed attained.