What is a Solid State Drive, and do I need one?

It is a type of flash memory based hard drive that has no moving parts. That makes them more shock resistant, silent and they have lower access times and latency, making them especially useful for holding the OS.
But they only really make sense if you plan to use read/write intensive applications in a professional environment, or for high end video games, and make no real sense for casual use such as you are planning, especially since their capacities are inferior to traditional hard drives and their cost is a lot higher as well.
Also, 32 Gbyte is not a lot of space, even for the OS.
They are also not as reliable as normal drives, and when they die, they will not die gradually like the old HDDs but suddenly and catastrophically, without any prior warning, so it becomes imperative that you make backups constantly.

@ragingloli has a good bead on it.
The SSDs are much much faster than a regular mechanical drive. But your usage as described does not really need the speed – mostly you’d notice the machine booting faster than it would with a disk.
I’d suggest the regular drive because you’d have a lot more drive space, 32GB is not a lot. If you expect to have a lot of photos that’s another good reason to get the disk instead of the SSD. You’ll get much more drive space for the $$.

I had a feeling that I might not be explaining everything right.

This one I’m looking at has a 6g RAM, 500g hard drive, and a 32g SSD.

Does that make any difference?

I think that one other advantage to the SSD is a much quicker boot time, if you often turn off the power and later do cold reboots. (I don’t; I normally keep my laptop running for weeks on end, only putting it in Standby when I’m not using it.)

But I don’t know that for certain; I don’t even recall where I heard it or if I trusted the source. Just something to check out. It makes sense, since there is no drive mechanism to read files during the boot, but on the other hand the boot process is about more than just opening programs and putting them into working memory, too.

@Seek_Kolinahr Oh! With two drives, one of which is an SSD, that could be a great configuration.
Hopefully the OS (Windows?) will be installed on the SSD and the machine will boot very quickly. If applications are also installed on the SSD they will open very quickly.
If you can verify that the OS is on the SSD out of the box, you can be assured this is a feature you will notice. Sweet !
With a 500GB disk you will have plenty of space for photos.

The basics are covered above, but one thing about SSDs is that they tend to be small unless you pay a lot of money. Since the one you are looking at also has a half-gig hard drive, you won’t have an issue, but some people make the mistake of getting a laptop with a small SSD and no hard drive.

It’s a good thing as an SSD will speed things up though.