Not a technical or in-depth description, but I once heard it explained like this:
Imagine needing to drive a train track spike into a railroad tie.
Single phase is like 1 guy swinging a sledgehammer hitting the spike- he hits it, then rests a bit, then hits it again.
3 Phase is like 3 guys of similar size/strength as the single phase guy- but they're standing in a circle around the spike, first one hitting it, then the next guy, and so on.
Not sure if this is a great example, but it helped me with my admittedly VERY limited understanding of 3ph vs 1ph.
One thing to consider if you buy any 3phase equipment for your home and you do not have access to 3ph power- you will need a converter to make the equipment work on your single phase power. The good ones can be VERY expensive. There are some DIY solutions, but you really have to know what you're doing to make them work- and even then they can cost $$$ if you have to buy the parts to make a converter.