TL;DR: Scroll to the last few paragraphs.
I've known about these non-mechanical storage devices for quite some time. It's probably rare to find some one who hasn't used a "thumbdrive"/USB stick/etc. But we are now in a era where almost all Apple products use SSD's or at least offer that option. So, what difference does that make?
The first difference is the extreme increase in disk access, of course! That's great and very welcome! Especially if that is where your operating system is stored. Start ups now take seconds instead of minutes!
However, another major difference may not come for you for years. That difference comes when you need or want to replace the SSD or the device that uses an SSD. The current versions of Disk Utility won't be of much help if you decide to reformat or "wipe" an SSD, although it will still be used.
Behind the scene, SSD's work a bit differently than a mechanical hard drive. A hard drive usually tries to store data on areas closest to where the read/write head usually "parks". That makes reading and writing to the spinning disk as fast as possible since the head doesn't need to move as much.
An SSD doesn't have a mechanical 'read/write head' to move, it is simply a (large) group of electronic memory cells with individual 'addresses' kept in another portion of memory. That bit of memory is very similar to the 'directory' on a hard drive. That's the part of the drive that apps like DiskWarrior repair on a hard drive. But in an SSD, this address/directory is just like the memory installed in your device. It is extremely fast to access these memory cells since it is all electronic.
However, these memory cells are not magic! They can retain information for a finite amount of time. In effect, these cells lose a tiny bit of capability every time they change the data in them. So, the old method of storing data on a disk in a particular bit has changed when dealing with an SSD. Instead of always writing to the "closest" cell, the controller tries to use cells that have not yet been used at all. After all, it's no further to one end of the memory area than to any other part because the path is not mechanical but electronic.
OK, so now you want to sell or donate or simply destroy the device with the SSD. How do you erase those cells?
Your old faithful Disk Utility app shouldn't even offer to try, but it will seem to, anyway. Remember that the SSD controller wants to use absolutely every unused cell before it reuses a cell (if it can). So, if you tell DU to "zero out" all memory, the SSD controller will simply mark Unused cells with "zeros". But what about the previously used cells?! Those previously used cells will simply have a note added to the directory saying they are no longer available.
Unfortunately, the data in those cells was not changed. They still hold the text, number, password, or whatever was stored there. The OS will not be able to read that data, but it is, in fact, still there. Hackers or others who take possession of the drive
do have ways of reading that data! Hopefully, that data is not of importance to any nation on Earth, but the whole point of erasing your data is still relevant.
Fortunately, there is a fairly simply method to destroy that data and it is built in to the OS! It's called "cryptographic erase". Remember FileVault? It's right there in System Prefs! You may never have used it but enabling it will make it next to impossible for anyone to make use of the data on the SSD (just like it does on a standard HD).
To make this long thread a bit shorter, the solution is to encrypt the SSD and then to use DU to "erase" it. What DU will actually erase is the encryption key that is stored on the drive. Without that key, the rest of the drive will be a collection of garbage bits of data!
Here are a few links for further reading and info:
