Before I get into the granular details I'll just come out and explain in simple terms, a hard drive in your computer is basically a stack of discs like what you used to put into a CD player. These discs are called platters and the internals of a hard drive reads and writes to them like you would when you burn a disc and then play it back. This is likely what you have storing all of the files on your computer.
A solid state drive or often called an SSD is a lot more like the flash drive you use to move documents from one computer to the other sometimes. This is made up of small memory chips that pass electricity through to retrieve the data. You might have one of these storing all of the files on your computer
So now that you understand on a basic level what a hard drive and solid state drive are we can talk a little bit more about what they do and how they differ. The first one I will cover is the hard drive. Like I explained earlier, a hard drive is basically a collection of discs stacked up all ready to be read and written to without needing to swap anything out. It stores data by magnetizing and demagnetizing specific areas. It is first split up into tracks which are the concentric paths around a platter. These are like the eight lanes on a running track, but on a hard drive there are many more than 8. Then the tracks are further split up into sectors.
Continuing with the running track analogy this is like the distance from the 0 to 100m being a sector and from the 100m to 200m being another sector. With this organization system it is much easier for the hard drive to figure out where things are because it can be directed to the correct track and sector and then look in that specific area for the data. Just like a runner on a track it takes the platters a little bit to process and start spinning and get to the destination. This delay before any data can be transferred is caused by a few things. First the read-write head must move to the correct track on the hard drive. Then the platter must be spun to the correct sector to grab the data. The time it take for the read-write head to move to the correct track is called the seek time and the time it takes on average to get to the correct sector is called the rotational latency. This delay means that it is not as good at handling lots of random bits of data but it is good at dealing with continuous writes and reads. This is why it is very beneficial to defragment your hard drive every once in a while. It organizes your data into a less random layout so that the platters can be read faster without needing to do as much track seeking and sector searching.
The measurement of how many random operations a storage device can do is usually measured in IOPS(input/output operations per second). As stated, these are relatively low for hard drives, they likely will not exceed a couple hundred IOPS. On the flipside, their throughput, the measure of their sustained reads and writes is pretty good. This means that if you are doing a large backup and just copying all of the files over the drive can just go from track to track copying everything relatively quickly. These are measured in MB/s(megabytes per second). For hard drives, these will also likely top out somewhere a little bit above the 200 MB/s range. So they have low IOPS and decent Throughput, so why does everyone still use them? The main reason is that they are still kings when it comes to capacity and cost. Capacities go all the way up to 12TB and larger is still on the roadmap. While cramming 12TB in a single drive they are still relatively affordable. A 4TB drive can be had for roughly $100 USD and for many people this is way more storage than they will ever need. A common metric people look at is price per GB(gigabyte). For hard drives like the 4TB at $100 it is a very impressive $.025/GB.
Now that we have thoroughly covered hard drives we can move onto SSD's. The biggest advantage SSD's have is speed. Every which way you look at it, SSD's are faster. Their IOPS are off the charts in comparison to hard drives. While hard drives were in the range of a couple hundred, SSD's are in the neighborhood of over 100,000 for some of the faster ones. This is partially because they do not have to spend any time searching tracks or changing sectors. There are no moving parts, it is simply the time it takes to process the request and the electricity to find the right part. At the same time, the throughput is very high. These devices are so fast that they have maxed out the capacity of the interface used to traditionally connect hard drives and some have moved to slots directly on the motherboard.
The fastest SSD's can push a throughput of 2000+ MB/s. Ten times faster than the fastest hard drives. Another advantage of SSD's is their heartines. Because they have no moving parts like a hard drive has, they can endure more vibration, impact, pressure and temperature. They are incredibly reliable devices now that can last 10+ years while many hard drives will not make it past 5. The SSD's downfall, at least for now, is the price per GB is relatively high and they do not come in sizes comparable to hard drives without costing an arm and a leg. You can expect a single 1TB SSD to cost over $200 even if you get a great deal meaning that the SSD's GB/$ rate is 8 times that of the 4 TB hard drive.
So in summary, SSD's are the pure performance king but currently cost quite a bit more per gigabyte so they are mostly best for applications where extreme speeds are needed. Hard drives are still widespread and have a legitimate space in many applications. Any application where lots of storage is eaten up like video and audio is a good place to use hard drives instead of SSD's if you cannot swing the budget for them.