Why do commercial flights turn / bank so sharply?
Airplanes are expected by air traffic control to turn at a "standard rate of turn" which is 3 degrees per second.  This will provide a 90 degree turn in 30 seconds.  A standard rate is used so that controllers can anticipate how long it takes for an airplane to turn to a heading and they can line them up easier.  It also makes the turn happen in a smaller amount of airspace so that two airplanes can be flying in the same general vicinity without getting too close.

Unfortunately, at the speeds that jet airplanes travel this would mean a very high angle of bank.  A standard rate turn at 200 KT TAS is about 30 degrees of bank and jets can go much faster than this, which would require even higher bank angles.  They actually limit it to 25 degrees of bank when using a flight director, mainly for passenger comfort.  

It can be impressive when looking out the window and seeing the ground, but don't worry, the airplane is more than designed for it!

This is used mainly at lower altitudes where there are lots of airplanes.  Once they are up high and airplanes are further apart (and the turns are also usually smaller) they  can bank even less (by using a "half-bank" mode) which adds to passenger comfort.