Her teacher asked this question to my niece (8 years old)? However I couldn't find a solid answer either. In which part of the flight, the effect of the air resistance (drag) is more important? Takeoff, cruise, descent or landing?
The answer they are looking for is probably cruise. This is generally the longest part of the flight, so the losses from drag will add up. Most aircraft are optimized as much as possible to have good performance in cruise to save fuel and meet range requirements, so having low drag is more important in this part of the flight than others. This is also generally the section where the aircraft is traveling fastest. As Peter Kämpf showed, drag is highest at higher speeds, other than periods where landing gear, flaps, etc., are extended and add more drag.
As Jay Carr explained, drag is important at every point while the aircraft is in the air, affecting different areas of performance. During takeoff, drag will affect the runway distance needed, and initial climb performance. Low drag during descent is helpful, unless you need to get down faster, like in an emergency descent. Drag is probably highest during landing, because the emphasis is placed on having as much lift as possible at slower landing speeds, and this lift is created at the expense of higher drag.
The question leaves a lot of room for interpretation, so here is my version:
If we assume a constant mass of the aircraft, resistance varies with speed, and there is a minimum relative to the lift force when the lift-induced and zero-lift drag components are equally large. You can now argue that air resistance (however defined) is least important at that speed and becomes more important at low and high speed.
The plot shows the drag components of a typical glider in straight flight, but if you adapt speeds and forces, the same plot works for any other airplane. It shows that the drag (= air resistance) is highest at the highest flight speed.
Anytime air is moving over the surfaces of the aircraft, drag is important. There really isn't a time when it's "more" important. When an aircraft wants to move, during any phase of flight, the thrust of the craft must exceed the drag the air (or wheels, on the ground) is creating on the craft. At any point that the aircraft is flying, the drag must be overcome to the point that the wings can create the required lift to get the aircraft into the sky.
Perhaps, though, the question actually had to do with air brakes? When those are deployed the amount of drag created is increased by quite a lot, slowing the aircraft by quite a bit. And as a result air brakes are often used during the descent phase of flight in order to keep the plane from accelerating to much as it approaches the runway. Perhaps that's what the teacher is after...
Drag (Air resistance) plays a part in all phases of flight, its most critical during takeoff or landing as this is when it will have the most drastic/immediate effect.
I would pick landing as my favourite for the answer and as it is the most apparent, with all the bits of metal hanging from the aircraft.
As the aircraft slows it lowers the leading edge slats(if fitted) and trailing edge flaps to increase the amount of lift the wing is able to produce, as you increase the lift you are also increasing the drag. In jet aircraft the spoilers are often used to assist this reduction in speed or to maintain/increase the rate of descent whilst decelerating(not easy in a heavy jet with lots of inertia). At some point during the approaching (normally around 2000ft ish) you have to lower the gear, which again adds to the drag.
All this drag on approach allows the engines to spool up, which is useful on large turbine aircraft as it means the engine is at a good state to provide power quickly in the event of a missed approach.
On touch down the configuration changes again - the spoilers deploy, reverse is selected and as the nose lowers the wheel brakes kick in - lots of drag (ok, the wheel brakes don't provide air resistance, but they are a fairly large part of the decel process). The spoilers drastically reduce the lift of the wing pushing the aircraft down onto runway meaning the brakes have the greatest effect. Some aircraft at this point change the flap configuration, in light aircraft its an option to retract the flap which reduces the lift on the wing making the brakes more effective. Other types lower more flap, having a "barn door" type effect. The Boeing 747 retracts the inboard section of slat, which again helps reduce the lift on the largest part of the wing.
As all this is happening thrust is redirected forward and power is increased on the engines helping the deceleration down to around 80-60kts.
In some aircraft (normally fighters) you hold the nose off the runway on landing to increase drag, braking aerodynamically down to a low speed. In commercial aircraft you normally lower the nose as the wheel brakes have greater effect (you normally have a lot more main wheels/brake units than fighter types).