Technically "Rise and Fall" refers to the up and down (vertical) movement of the dancers' BODY. "Rise and Fall" is accomplished through the actions of the foot (ankle), leg (knee) and the body (stretching).
The ankle is used to lift the foot from the flat position to the ball position (Rise) and lower the foot from a ball position to a flat position (Fall). The knee bends the leg to create "Fall" and straightens the leg to create "Rise" (There is no rise in the legs without first lowering/falling). The body can create "Rise" simply by stretching and "Fall" by relaxing.
The term "Rise" is often misused. For example, let's look at Foxtrot. Technically Foxtrot has no "Rise" and "Fall". Instructors often talk about ankle "Rise" in Foxtrot. There is the same ankle action (as described above) but it does not result in the upward movement of the BODY. As the ankle lifts, the knee bends to neutralize any upward movement of the BODY. It is an ankle action but it is not "Rise", by definition. Foxtrot's character is a very even, smooth, gliding movement with no "Rise" or "Fall". It is very important that you know exactly what your instructor is trying to communicate to you.
On the other hand, the character of Slow Waltz is defined by "Rise" and "Fall". The first step (beat 1) has a lowering action ("Fall") and the "Rise" occurs during the second step (beat 2). The "Rise" is created by lifting the ankle, straightening the leg and stretching the BODY all at the same time. The "Fall" is executed during the third step (beat 3). The "Fall" starts by lowering the ankle, then bending the knee and then finally by relaxing the BODY.
Viennese Waltz, unlike Slow Waltz has no "Rise" and "Fall". There isn't enough time. The characteristics of Viennese Waltz are quick half turns and a swaying action. The footwork contains ball steps, but they don't go to a flat foot position.
Tango (American/International style) has no "Rise" and "Fall", the footwork has no ankle lifting action and the knees stay in a slightly bent position. The characteristic of Tango is a powerful, flat, staccato type of movement.
Latin/Rhythm dances have no "Rise" and "Fall". There is ankle action similar to that described above except that the ankle action creates a horizontal movement of the BODY instead of a vertical movement.
Bolero is often referred to as "The Latin Waltz". It does have "Rise" and "Fall", however, there is no foot (ankle) action. The "Rise" and "Fall" is accomplished only through the legs and body. In Slow Waltz the "Rise" accommodates the free leg closing to the supporting leg. Bolero accomplishes this by lifting the free legs' hip up inside rib cage allowing the free leg to close.
Ballroom Two Step has "Rise" and "Fall" also, but it is executed in a slightly different manner. There is what I call a "pole vaulting" action on the second step that creates the "Rise" and a normal "Ball/Flat" action on the third step allows the "Fall". The second step footwork is a "Ball" only step causing the leg to be longer. As the BODY moves over the long leg it is lifted up (pole vaulting action).
Samba doesn't have "Rise" and "Fall" either. Its primary characteristic is a "pendulum action". It does have a "Ball" only second step. This creates a long leg that develops the pendulum movement front-to-back and side-to-side.
East Coast Swing and Jive don't have "Rise" and "Fall" either. There are ball/flat steps but the vertical movement of the BODY is negated again by the soft knees.
Understanding "Rise" and "Fall" and dancing it correctly, is an important of part of the lead and follow process. It is also a major part of defining the character of the dance and giving the dance its unique feeling.