An oscillatory movement happens when the direction of movement periodically alternates, but the trajectory is the same for both directions. This is the case with pendulums and strings of guitars, for example.
The figure below represents a vibrating rope, note that even moving down and up from the point of origin always keep equal distances from this point.
If we consider that the body begins to vibrate from the darker line, each time the rope passes this line, after traversing all the other lines considered, we say that it has completed a cycle, an oscillation or one vibration.
As with periodic movement, the interval that elapses for a cycle to complete is called movement period (T) and the number of complete cycles in one unit of time is the oscillation frequency.
If you've been to a tall building, you may have noticed that on windy days your structure rocks. It's not just printing! Some large structure constructions such as buildings and bridges usually sway from the wind. These vibrations, however, happen with a period of oscillation longer than 1 second, which is not of concern. A building could only be damaged if it had a natural vibration with period equal to the wind vibration in place.