Bounds represent the points with which data cannot exceed, such as minima or maxima.

Bounds are mathematical limits to data points which may influence their properties. Lower bounds represent points with which data from a set cannot be lower than, whereas upper bounds are those which data from a set cannot exceed. If we see the following vector below:

$$ \begin{bmatrix} 2,3,5,10,22,48,96,107 \end{bmatrix} $$

The values $2$ can be considered the lower bound whereas the value $107$ can be considered the upper bound. A real world example of a lower bound is the number of car crashes at an intersection. Drivers cannot get into negative car crashes, so constructing mathematical models based on this kind of data may require careful consideration, such as the limitations of predictions when entered into regressions. Another example of these bounds may include confidence intervals, which set an upper and lower bound to what sampled data may be.

Some basic info about mathematical bounds can be found here.