The length of a badminton racket is measured from the bottom of the racket handle/grip to the tip of the racket head. See illustration above.
A typical racket length is between 665m to 675mm, and should not exceed 680mm. A racket with length between 674mm to 680mm is sometimes labeled as 'extra long' racket, because a lot of rackets are around 665-670mm in length.
A longer racket will give you better power compared to a shorter racket. The reason for this is due to the law of physics, analogous to when you are sweeping floor with a broom. You definitely use less strength with a long broom, compared to a shorter one. However a longer racket will hurt the maneuverability of the racket a little. To experience this, try holding a racket closer to the racket cone (the triangle intersection where the grip meets the racket shaft) and flick the racket around. Then try repeating this by holding the racket far lower to the grip, to simulate a longer racket. You will feel that it’s harder to flick the racket this time.
It is not really too important to consider the racket length when you choose a badminton racket, but sometimes, the slight extra in the racket length might help increasing the power relatively. However do remember that the extra length will hurt the racket maneuverability to a certain extent. As a general tip, any racket within the length of 665 to 675mm will normally serve you well.