If your chain rubs against the front derailleur when you are climbing out of the saddle or pushing hard on the pedals, that's a flexible frame. If your teeth rattle over bumps and you feel every frost crack or pebble on the road, that's a really stiff frame. You don't lose pedalling energy from flex with a stiff frame, but you give up a bit of comfort.
Bike manufacturers tend to make their race models stiff and their sportive type models a bit more flexible. Some designs aim to have vertical flex for comfort (the bike flexes upwards over rough surfaces with lateral stiffness to get the most efficient pedal stroke.