Understand storage
When someone asks, "How much memory does that computer have?", exactly what they mean isn't always clear. Computers need memory in order to think about what they need to compute. This type of memory, random access memory, is also called short-term memory. But what if you want to turn off your phone or laptop and come back to something later? Well, you need memory for that too. People use the same word for two different things!
Long-term Storage
The second type of memory is more accurately called "storage" or long-term memory. The first type of memory, RAM, is only active when the computer is on. Once the computer is off (or a battery runs out), whatever is in RAM goes away. Long-term storage is different, storing data on stuff that doesn't need power.
For example, when you want to remember items for a grocery list, you may write it down on paper and take it with you so you "don't forget." You take something from your short-term memory (your brain) and put it on something that will last (your list) even if you lose it from your memory. You can go to sleep and pick up your grocery list in the morning and take it shopping.
Types of Storage
The stuff used for storage is varied, but the two main types we'll look at are magnetic storage and digital storage.
Hard Disk Drives
Early computers often used magnetic tape to store their stuff. This tape was similar to the audio tape used to record and play back music. One disadvantage of tape was that computers couldn't get to any data on it "randomly." Computers had to rewind or forward through the tape to get to the spot they needed. This could be a slow process.
Then came disks that spun fast and used an arm and head to read and write information (sort of like a record player). This is called a hard disk drive, or HDD. These use little magnets to hold data like a tape does. Unlike tape, though, HDDs are much faster, don't break as much, and let people get to information rapidly, regardless of where it is on the disk.
Hard disks are still used, though people use them less since the physical size and cost of the second type of storage, solid-state drives, have come down while the amount they can store has gone up.
Solid-state Drives
Solid-state drives (SSD) have no moving parts. They store data on small circuits as opposed to magnetized disks. Since they have no moving parts, they tend to break less, are lighter, and tend to be smaller. Many SSDs are faster and last longer than hard disks. Solid-state disks also tend to use less power.
Similarities
Both hard drives and solid-state drives can hold a lot of information. Some of the biggest drives can hold terabytes of data.
If you printed all the data just one of these drives can store and stacked the sheets on top of each other, the stack would be taller than the tallest building in the world!
These drives also connect to the computer in similar ways, so people can use one or the other without having to buy a new computer.