Redstone dust acts as an electric wire, which transmits charge if you stand on a pressure plate, flip a switch or press a button. The red torches are redstone torches. They are always on, but when you send a charge to a redstone torch, it turns off. Basically it's a NOT gate, but one you can use as both an input and output.
There are so many because charge will only travel 15 blocks along redstone dust, but you can set up a series of torches to extend this.
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