There are two things about electricity you need to understand.
1) It moves easily through metal, especially copper. Wires are made of copper. It does not move through plastic. That brown stuff around the wires is plastic. It does not move through air. It will move through you if you give it a chance but you really don't want to do that!
2) In order to move it must have somewhere to go. It will not move along a piece of wire if the end of that wire is surrounded by air. Think traffic jam. If the car at the front runs out of road, the ones behind it can't move either.
So far so good. Now for the tricky bit. Electricity is sitting in the live wire that comes into your house. It's come all the way from a substation through a live wire under the street and it would like to go back home along a neutral wire which is also under the street but it can only move through metal; not plastic, not air, just metal.
It can move along the brown wire in that cable marked "supply" until it reaches that thing in the middle. That thing is a terminal block and, although they aren't explicitly shown, there are four metal barrels in it which allow electricity to pass freely between wires on opposite sides. The spaces between the barrels are plastic so no electricity can pass from one barrel to another.
Let's follow the brown wire coming in on the left hand side of the top barrel. It can pass through the barrel to either of the two brown wires on the other side. It can go along either or both. Think traffic again. When a road branches, cars can take either route. One brown wire goes into another cable marked "supply to next". We aren't interested in that one. The other brown wire goes to the switch. That's how electricity gets to the switch.
What happens next depends upon what you do with the switch. What you have in there are two pieces of metal that are either touching if the switch is on or separated by air if the switch is off. Electricity does not move through air so if the switch is off there is nowhere for it to go. Let's switch on. The electricity can now move freely into the other wire in the switch. The one in the diagram is blue with a brown sleeve. Yours is brown. It doesn't matter. Electricity doesn't care what colour the plastic is!
Follow that blue wire and you'll come to the bottom barrel in the terminal block. Electricity can move freely through the metal barrel to the brown wire on the left hand side. It cannot pass through the plastic to the barrel above. The brown wire goes to the light bulb, inside of which is a very long piece of very thin wire. That's the filament. It doesn't look very long but if you use a good magnifying glass you'll see that it's wound into a spiral - and that spiral is wound into a bigger spiral. It's long!
So now we've reached the light, but there's more. No electricity will move anywhere unless there is somewhere for it to go. At the other end of the filament is the blue wire. Follow that back and you'll come to the barrel second from the top. There are two wires on the other side of that barrel. Which way, if any, will it go? There is only one way. The wire to the right may go lots of places but none of them are the way home. The only way home to the substation is to the left along the wire in the cable marked "supply" because that one goes back to your fuse box and from there out to the neutral wire in the street.
Can you see it now? With the switch closed there is a continuous line of metal - that's called a circuit - from the substation through the closed switch and the light bulb and back to the substation. It goes substation live side -> wire -> fuse -> wire -> barrel -> wire -> switch -> wire -> barrel -> wire -> filament -> wire -> barrel -> wire -> substation neutral side. You'll notice that a fuse has appeared in the list. That's not on the diagram but it will be there - in your fuse box.
Thus endeth the first lesson. Read it until it makes sense. It's not rocket science. Well maybe it was in Faraday's time but today's kids learn this stuff in junior school.