When you seethe, you're so angry and bothered that you feel like you're boiling. In other words, to seethe is to feel very angry, as if your insides are bubbling.
Seething is usually something you do on the inside. You might say nothing or do nothing while you seethe, but inside, you feel so upset that you're warm or hot with anger.
If something terribly unfair happens to you, you might sit quietly and seethe over what happened.
Usually it's people who seethe with anger, or seethe over bad things that happened. But water can seethe, too, meaning it bubbles, foams, hisses, or boils.