The simple answer to why chilli is spicy is that many capsicum plants produce capsaicinoids, most importantly capsaicin itself. These chemicals trigger mammal’s (TRPV-1, transcient receptor potential vanilloid, type 1, if you must know exactly) nerve receptors that sense different dangers, especially heat.

The capsaicinoids are so-called secondary metabolites. They are not necessary for the survival, for the basic (primary) living processes of the plant. They do, however, help the plant against diseases, in the first step.

Secondly – and here it gets really interesting – chile pepper plants “found” that producing capsaicin(oids) in their fruit prevents the fruit from being eaten by mammals, while it causes no issues for birds.

This is what the chilli “wants” in the wild: For its fruits to be eaten by birds, which will poop out the intact seeds (plus fertilizer) under other bushes where a new wild chilli plant can grow very well. And not to have hungry mammals, which will destroy the seeds by chewing or digesting them, eat them instead.

So, the chilli became spicy because that helped it to fight off diseases and hungry mammals – like humans. And it tastes spicy to us because we are mammals, thus we have the nerve receptors which get activated by capsaicinoids and cause the “burning” sensation of a hot chilli.