What two factors determine how far from the shoreline waves will begin to break?
Wave length/height and seafloor slope
A wave transmit energy through the water but there is no actual transport of water until the waves breaks.
The point at which a wave breaks is determined by the depth of the seafloor and the height (H) and length(L) of the wave.
A wave approaching shallow-water increases its H and reduces its L until a critical H/L > 1/7 is reached.
At this point the wave becomes unstable and breaking occurs. This is also called the "surf zone".
On steeper slopes the H/L ratio increases faster leading to formation of surf.