"When the rays of light starting from a point travel in different directions, then the collection of such rays is termed a divergent beam of light. ex a magnifying glass will narrow the light beam. The bulb is at focus of the concave shape. so emerging beam is more of parallel beam than converging. 
"When the rays of light coming from different directions meet at a point, then the collection of such rays is termed a convergent beam of light."eg. a painted picture drawn on the surface of a flat frosted glass

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When rays are diverging from a source of light,  they are spreading out as they travel, then they are divergent rays.

   Rays that are coming out of a common electric bulb.
   Rays that are coming out of a concave lens.
   Rays that are coming reflected from a convex mirror.

When rays are converging towards a point as they travel forward, then they are convergent rays or beam.

   Rays that are coming out of a convex lens.
   Rays that are reflected from a concave mirror.

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