Here's another example - say you want to carve off the end of a cylinder.

To do that you might draw a curve in a side view that is positioned to intersect it visually, like this:



If your cylinder is an open surface, it might look like this:




You can use Boolean Difference to cut that cylinder surface up using the curve as the cutting object, which will cut it into pieces like this:



Then if you delete the end piece you'll see that you still have an open surface:




However, if you have a solid cylinder that has the ends capped off, it would look like this:







When it's a solid the booleans know how to combine the pieces together to keep the result a solid, which can help to avoid trying to manually build the side wall pieces.

- Michael