Solid State versus Hard Drive

It may be time for a new computer based on the fact that I would need to pay over $200 to get a 1 year extension of my warranty. I'd probably keep the old laptop and use it to learn Linux while transferring all my pop-culture stuff to the new computer.

I think I want a laptop again, but I'm noticing that there seems to be a choice between solid state and hard drive. Can someone outline the differences for me? I'm not a hardware girl, but I know it influences my ability to run programs and connect efficiently to the internet.

What other things should I be looking for? I assume setting up the new computer with most of the storage space in external drives is better, but I could be wrong.

Help me hive mind. *G*