Learn Dutch: Het anker gaat omlaag. - The anchor goes down.

Both omlaag and naar beneden mean "down" or "downward" and are often completely interchangeable when talking about direction. omlaag is very common with verbs of motion like gaan (to go).

Could I just say "Het anker gaat beneden"?

No, because beneden describes a fixed location, like being "downstairs" or "below". Since the anchor is actively moving, you must use a directional word like omlaag or naar beneden.

Does omlaag come from the word laag (low)?

Yes! The word laag means "low", and adding the prefix om- gives it a sense of direction. So omlaag literally means "towards low" or "downwards". You will also see this in its opposite: omhoog (upwards), which comes from hoog (high).