To try put these concepts as simply as possible:
Segmentation is the process where memory (RAM) is allocated out in chunks called segments. This allows an application to store various parts of itself and the data that it's working on in different parts of RAM.
Imagine you have a big warehouse, but rather than just having a big empty space you subdivide it by filling it with shelves. As an application needs storage space the Operating System assigns it shelves that it can use, but these shelves do not necessarily need to be side by side. So long as the application knows that it owns shelves 567, 3214, and 5678, it can use that space as it sees fit.
Paging is the process where memory is moved from one medium to another.
So imagine you have two warehouses. One next to the dock (RAM) where you can process shipments quickly, and one in town (Hard Drive) that's considerably larger but slower.
The warehouse at the Docks is fast so you want to use it as much as possible, but it just isn't big enough to store everything. So you move contents that aren't needed today out of the way and store them at the other facility until they are needed. The down side being that it takes time and effort to move stuff back and forth all the time.