Fair question
If you simply type in at Google
what is a server
... you can read for ages.
One I found quite good was
https://www.techopedia.com/definition/2282/server
If you wanted to network those old computers of yours and have them in different parts of the house, then you might choose one to be a Server, and it can feed "content" to the other PCs.
In a home environment the Server rig does not need to be the biggest fastest newest one with the most grunt, but it needs to have a fair bit of memory and to be RELIABLE. You may want the Server to be on 24x7, even if you switch the other computers off overnight.
You were confused a little elsewhere with the difference between memory and capacity.
Your 350 GB hard drive is your capacity, for operating system (OS) software and storage. Like your body, it might be small (4'11") or long/tall (6'6"). Your CPU (central processing unit, or chip) and your RAM (Random Access Memory) are like your brain and memory. You might have 2 - 4 gigabytes of RAM, or some rigs can have 16 - 32 GB RAM (I have 16 GB on this Dell).
A computer chosen to be a Server can get server software installed on it, the most notable is probably Apache.
Linux Servers are the best in the world, and as Walter Brennan used to say in The Guns of Will Sonnett "That's no brag ... just fact!".
If you find any company that relies on say more than 100 computers being up and running, and they are not running on Linux servers ... they likely need their heads read.
Cheers
Wizard