At the light hit from an external light source on the fibre butt-end a few waves (rays) which spread on fibre regardless of initial ray are excited in it. Possible (allowed) own light waves which spread through fibre name mode. In fact, it is also the possible trajectory of light ray passing through optical fibre to name a mode.
In multimode fiber fibre large number of modes possible exists as a result of comparatively large core diameter and using noncoherent light sources. Fiber supporting only one mode is called single-mode fiber. Such effect can be reached using using coherent light sources (lasers) and core diameter closed to wavelength.

In a step-index multimode fiber, rays of light are guided along the fiber core by total internal reflection. Rays that meet the core-cladding boundary at a high angle (measured relative to a line normal to the boundary), greater than the critical angle for this boundary, are completely reflected.
Rays that meet the boundary at a low angle are refracted from the core into the cladding, and do not convey light along the fiber. The critical angle determines the acceptance angle of the fiber, often reported as a numerical aperture. A high numerical aperture allows light to propagate down the fiber in rays both close to the axis and at various angles, allowing efficient coupling of light into the fiber. However, this high numerical aperture increases the amount of dispersion as rays at different angles have different path lengths and therefore take different times to traverse the fiber. Step-index fibers are mainly used in spectroscopic applications.

In graded-index fiber, the refractive index in the core decreases continuously between the axis and the cladding very close to a parabolic relationship. This causes light rays to bend smoothly as they approach the cladding, rather than reflecting abruptly from the core-cladding boundary. The resulting curved paths reduce multi-path dispersion because high angle rays pass more through the lower-index periphery of the core, rather than the high-index center. These graded-index fibers are mainly used in telecommunication application.

Single-mode optical fiber with a core diameter less than about ten times the wavelength of the propagating light cannot be modeled using geometric optics. Instead, it must be analyzed as an electromagnetic structure, by solution of Maxwell's equations as reduced to the electromagnetic wave equation.
The most common type of single-mode fiber has a core diameter of 8 to 10 mkm and is designed for use in the near infrared. The mode structure depends on the wavelength of the light used, so that this fiber actually supports a small number of additional modes at visible wavelengths. Multi-mode fiber, by comparison, is manufactured with core diameters as small as 50 microns and as large as hundreds of microns.