So so much is the deal with redstone, more than I could type here and far more than I even know. Basically it is like electricity, stuff can be turned on or off using it with the different things powered using redstone dust which is the equivalent to wires. There are logic circuits you need to know like an 'and' or an 'or' gate etc. up to more complex circuits like pulse extenders and clocks to t flip flops and rising or falling edge monostable circuits. Now these wont mean anything to you yet but you can start piecing them together to create more complex circuits as a pulse extender in a pop up bridge is the same as the one in a mob spawner. If you get more in to it you will find that you stop thinking in terms of I need some redstone dust, 4 pistons, 3 blocks, 5 repeaters etc. and start thinking I need a t flip flop to power this pistone but also power a pulse extender which goes into an inverted falling edge monostable circuit. The video my opening post really does do a good job of explaining the basic of redstone though expect to have to watch it several times, I did and I've played around with redstone in the past.
As for things to build, the most useful for any minecraft is semi or fully automated farms. These can be simple food farms which allow you grow and harvest food very fast through to bigger animal farms or even massive mob farms. Automatic sorters are useful too especially for big mob farms so all your zombie flesh goes in one chest, bones in another, gunpowder in a third etc. without you needing to do anything.