Anything that you have data being accessed from multiple computers could be considered a server. It's a loose word that can describe a web server, email server, data server, application server, database server, etc. Mine is an all purpose server because I use a lot of server services but none of them require a dedicated box because there isn't enough traffic.
My server is simply a server-class rackmount case with all the computer components you need (CPU, motherboard, memory) and the case happens to have 16 hot-swappable hard drive bays. I have them all filled with 500GB drives. Then, I have a Promise RAID card (PCI-express) which plugs into all 16 of the drives and gives me a 7TB data drive. It is actually 8TB (8 * 500) but two of the drives go to parity. So, if two drives fail, I won't lose any data.
Unfortunately, I'm literally almost out of free space. So I am contemplating building a new 21TB server. I want to find a buyer for this one, first, because otherwise it may just sit--what a waste. I had about 1.3TB free up until perhaps 8 months ago when it started diminishing quickly. I'm down to about 100GB free right now--out of 7,000 total gigabytes.