The speed at which the aircraft will fly is lower, but it may take more time to reach that speed because of the extra drag. The change in distance depends on the specific aircraft, as will the amount of flap the manufacturer would recommend for takeoff. If it lacks power - such as a loaded Cessna 172, the amount of flap deflection suggested for takeoff will be very small, and more proficient pilots have been known to accelerate without flaps, then lower them when they have reached the flaps down flying speed.
Had they used full flaps all the way, the extra drag would reduce acceleration so that it would take longer to reach even the lower speed now needed. On aircraft with more power, more flap deflection is possible, always balancing the additional drag with the reduction in acceleration. 
Presumably this section needs to be rewritten to make it clearer.