To cook grains (e.g., to cook rice) by heating with water; commonly used for cooking rice.
毎朝、父が美味しいご飯を炊いてくれる。
Every morning my father cooks delicious rice for us.
炊飯器で白米を炊く時間は機種によって違う。
The time to cook white rice in a rice cooker varies by model.
炊きたてのご飯は香りがいい。
Freshly cooked rice smells great.
In Kansai dialect, it can mean to boil, simmer, or stew (a broader sense of '煮る'), e.g. to simmer vegetables.
関西では大根を甘く炊く料理がよく出る。
In Kansai they often serve dishes where daikon is simmered in a sweet sauce.
この鍋で野菜を炊いてください（＝煮てください）。
Please cook (simmer) the vegetables in this pot.
Internet slang/informal usage meaning 'to get angry' or 'snap' — a figurative, colloquial sense.
あの書き込みを見てめっちゃ炊いたよ。
Seeing that post really made me angry.
彼の態度に炊いて、思わず言い返してしまった。
I got so angry at his attitude that I snapped back.