The beat is the basic unit of time in music often characterized by a repeating sequence of stressed and unstressed beats (often called "strong" and "weak") and divided into measures. (Wikipaedia defn.)
A rhythm acts to draw the eye across the page and is dynamic in nature.
|Trees and Shadows, Pittencrieff Park.|
In this simple picture of trees in the park the repetition f the trunks and shadows forms a rhythm which leads one though the picture, this is emphasised further by the diagonal line formed. Both work together to encourage the eye to look to the end of the line of trees.
|Glasshouse Roof, Edinburgh|
The repeating and interlocking shapes of the roof supports form a rhythm, that takes you across the image, it is again enhanced by the diagonal line formed by the points of the structure.
|Malleny House Fountain|
Here the rhythm is formed by the decreasing circles in the reflection, which leads the eye to the bottom of the image and then back to the top.
|Reeds in the Wind.|
The reeds waving in the wind give a rhythm, but tends to take the eye from right to left, rather than left to right, which creates an tension in the image in spite of the calmness of the scene.
The roofs set up a clear rhythm her - starting from the side of the building and leading the eye around the corner and into the distance, this gives the image a 3-dimensional look.
Once you start looking for them rhythms are everywhere in pictures, some small and barely noticeable, some form the whole picture. They give a clear sense of movement and increase interest.