掟 (おきて, okite) means a solemn rule, law, or decree, often with an old-fashioned or mystical feeling. In the song, it refers to the “law of nature” separating the mermaid from the human world, which the singer defies by offering his soul. Its dramatic connection to forbidden love makes it especially memorable.
Janne Da Arc turn a love song into a fairy tale here. The singer is watching a mermaid swim free in an emerald sea, "エメラルドの海を自由に泳ぐ" (swimming freely in the emerald sea), and he can't stop listing what she looks like: cobalt-blue hair, sapphire eyes, a coral hair ornament and pearl earrings that are "君だけのドレス" (a dress that is only yours). The chorus keeps telling her "Miss Marmaid 綺麗だよ" (Miss Mermaid, you're beautiful). Yes, it's spelled Marmaid in the lyrics. Learn mermaid for real life.
Then the problem: "君を抱きしめたくても届かない" (even though I want to hold you, I can't reach you), because of "海と大地と自然界の掟" (the law of the sea, the land and nature). So he does something drastic. He has left behind everything he owns, and sings "今掟をやぶって魂をささげよう" (now I'll break the law and offer up my soul). It's a big, slightly over-the-top gesture, and that is the fun of it. Watch the word 掟 (okite), a rule or law you aren't supposed to break. By the end he promises "もう流すこともないよ青い涙" (you won't shed blue tears anymore), and the English outro says it again: "You don't have to cry".