How does a trailing edge flap actually help an aeroplane?
It just changes camber but what does that exactly do that’s beneficial?
Increase coefficient of lift - more lift for same speed, which can get one off the ground faster - or - same lift at a lower speed. This helps slow down for landing.
Increase drag - changes glide slope if your landing glide slope is "long". Higher flaps settings are especially useful for this.
Now, the fun part:
Moves the center of pressure of the wing rearwards. This will cause a pitching down tendency.
Causes a stronger downwash on the tail, creating a pitching up tendency. This is especially noticeable flying a high wing/low tail aircraft such as a Cessna 172, particularly at the higher end of the Vfe range.
Designers try to balance the effects of 3. and 4., but dumping full flaps could help raise the nose in the event of an elevator failure just before landing.