Originally, they were hidden behind a sofa, and later, the legs were shortened (so you didn't have to strain your neck to see who you were talking to) and they were carefully placed in front of the tea-sipping people. Designs changed depending on the year, but gradually they became a common piece of furniture in everyone's home.
I suspect the term "Coffee Table" began easily; coffee became more popular, and tea was considered more of a formal, delicate occasion. A cup of coffee wasn't confined to a particular time of day, or needed to be accompanied by a biscuit and a civilized chat.
To me, I think a coffee table, or side table, is mandatory in any space where we like to spend our time. Not just for coffee, but for putting things down on. I don't quite understand rooms that have sofas and chairs, but no tables. From a design perspective, it balances out the room, but more importantly, from a practical perspective, it gives you somewhere to put your stuff.
I think, now that I am writing this, that it also goes back to comfort; a room with tables welcomes you in. It speaks to you, and says that there is plenty of space for you and your coffee, to read a magazine, or curl your feet up for a moment. Without a table, it feels like you must sit up straight, and hold onto whatever you came in with. It can be awkward, and not very relaxing.
Tables also fill the gap. Have you ever sat in a room staring at the blank space in the middle, where it should have been? Analyzing the rug, and clutching your coffee and handbag; you can't put them on the carpet, because you know they will wobble, (or you will kick them over) and you wouldn't dare risk a wet ring on the newly finished wood floors.
When this happens, your host might scramble for something (usually a tray table and an apology) and you feeling even worse for clutching your cup so tightly in the first place. Not how anyone wants to spend their afternoon.
Maybe it is the gathering at the kitchen table that has gently moved the coffee table aside, or perhaps we got tired of "designed" rooms that felt too formal? I'm not sure, but I do think that the original intention made a lot of sense; if you're going to sit down, have a table....
Photograph from: www.vnuks.com and quote from www.thecoffeetable.co.uk