The space an object takes up or the space inside it
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The amount or volume a container can hold.
the amount of water in the pool (volume) somthing like that
Pi is important to the study of math because is can be used in many ways. For example, you can use it to find the circumference of a circle and the volume of a sphere. I am not really sure how people calculated that pi works for that, but it plays a big part in our math history.
There is no single formula for volume. Some simple shapes, such as a cuboid, sphere, cone, pyramid, prism have relatively simple, but different formulae. Other shapes have more complicated formulae.