Light striking the interfaces at less than the critical angle passes into the classing ans is lost. Ray of light do not travel randomly. They are channeled into modes, which are possible paths for a light ray traveling down the fiber. A fiber can support as few as one mode and as many as tens of thousands of modes. While we are normally not interested in modes per se, the number of modes in a fiber is significant because it helps determine the fiber's bandwidth.
More modes typically mean lower bandwidth.
The reason is dispersion. A pulse of light travels through the fiber, it spreads 9out in time. While there are several reasons for such dispersion, two are of principal concern. The first is a modal dispersion, which is caused by different path lengths followed by light rays as they bounced down the fiber. Some rays follow a more direct route than other.