Do you mean Random Access Memory (RAM)? If so, it is important to check this out before you purchase a new device as it determines how good the device is at multitasking. Generally, the higher the RAM the better the ability to run several programs concurrently. For Windows systems it is useful to note on this website whether your operating system is making the most of the RAM installed, click HERE
Hard drives are another kettle of fish in the memory/data world. For Windows desktops and laptops this is generally a C: drive which is installed within the device and is unremovable. It is where all your programs, documents, photos, music, videos etc can be stored and accessed so long as the device is turned on.
You can purchase external hard drives quite easily or use cloud storage nowadays; thankfully PC's usually come with enough storage for the average user.
Unfortunately if you own a Macbook Air the maximum storage that they can come with is 128 GB SSD. It is fast but could only store about 20* movies. So you would need to upgrade or buy and external SSD.
I think by memory, you mean the space the computer needs to run their programs. It's required when you get a new computer. In fact, I think when it comes to memory, the bigger is really the better. As for hard drive, it depends on how much you need for storage. The computer can still function without one. Or you can increase the storage capacity with a portable hard drive. Not very expensive, I think. Getting a computer with a large memory is much more expensive.