Rolling resistance is the energy that is lost when the tire is rolling. The main reason for the loss of energy is the constant deformation of the tire. Pressure; diameter, width, construction type and tread pattern all have an effect on rolling resistance.
Wider tyres (for example 25mm rather than 23mm) tend to have lower rolling resistance however narrow tires have an advantage over wider tires at higher speeds, as they provide less air resistance.
A bicycle with narrow tires is much easier to accelerate, because the rotating mass of the wheels is lower and the bicycle is much more agile.
The importance of this aspect becomes clear very quickly, when you ride in a fast group of cyclists and when you have to accelerate rapidly from 20 to 40 km/h after a sharp turn in order to keep up with the others.
Professional road racers are tending to ride wider tires more and more. Instead of the current standard width of 23 mm, the professional road racers choose more and more tires with widths of 24 or 25 mm.