A character is helpless if something says they are helpless.
A paralyzed character is frozen in place and unable to move or act. A paralyzed character has effective Dexterity and Strength scores of 0 and is helpless,
Unconscious creatures are knocked out and helpless.
A creature that is tied up is "bound" which means it has the Helpless condition.
A helpless opponent is someone who is bound, sleeping, paralyzed, unconscious, or otherwise at your mercy.
If the part about "otherwise at your mercy" is confusing to you, it just means that there are other conditions that cause helplessness. In such cases, the rules text specifically states that the character becomes helpless.
If the part about "held" is confusing to you, it's because there is no such thing as "held". There is "tied up", as described above, caused usually by being physically tied up (by ropes, chains, etc.). Grappled does not mean held, and does not cause helplessness.
Isn't the passage that the Dexterity is 0 partly redundant since a paralyzed creature has a Dex of 0 anyway?
Kind of. Not all helpless creatures are paralyzed. The paralyzed condition, yes, states that the creature has a Dex of 0. However, the sleeping condition does not state this outright. In other words, sleeping creatures also have a Dex of 0.