Eternals are what separate Eternal Sevens from the traditional Sevens (Fan-Tan) game underneath it. There are 22 in total, split into instant effects that fire once and persistent effects that change what is legal for as long as they are in play.
You reach them through the third of your three pass actions. Because every pass action is single-use, triggering an Eternal always costs you something — the question is whether the effect is worth a third of your total flexibility for the game.
These resolve immediately and are gone. Eleven of them:

The player who triggered this takes another turn.

Pass one of your cards to another player.

Choose a colour. Each other player gives you a card of that colour if they have one; you then pass one card back to each player you received from.

Each player passes a card to the left.

The next player's turn is skipped.

Move all star blocks to the opposite side.

All currently discarded face-down cards are revealed face-up.

The current player swaps their entire hand with another player.

Add one Rare card from the deck to your hand. In Standard mode, if no Rares remain and you hold fewer than two Additional Play Tokens, you gain a token instead.

Each player gains one Additional Play Token. A player already at the cap of two gains nothing.

Each player discards one card, starting with the current player and going clockwise. A player can finish this way.
These stay in play and restrict what can legally be done. Most of them cost you something, so the skill is in picking one whose restriction you can live with and your opponents cannot. Eleven of them:

You cannot discard cards from your hand, though you can still select the pass action.

If you have a Rare card you must play it. You may also pass even when you could play a card.

You may play a second card. If an Eternal action is triggered with the first card, the second is not allowed.

If you play a number card on top of a Rare already in play, you add that Rare to your hand.

Place a Must Play token on a field without a card.

Trigger the effect of the previous instant Eternal again.

You cannot place 3s or 8s — but you may play Rare cards on those fields.

You cannot place 1s or 10s — but you may play Rare cards on those fields.

You cannot place purple cards — but you may play Rare cards on those fields.

You cannot play Rare cards. You are allowed to discard them.

You cannot use Additional Play Tokens.
Dragon cards sit on top of the Eternal system in Expert mode. Each Dragon has a front and a back side with different abilities, and flipping between them is itself a decision — the back side is usually stronger but gated behind a condition you have to set up first.
Because a Dragon's two sides pull in different directions, they reward planning several turns ahead: you commit to a side before you know how the rows will develop, and a Dragon that was excellent on turn three can be dead weight by turn ten.
Beginner plays the core game with no Eternals. Standard introduces the Eternal pool and the wider pass effects. Expert adds Dragon cards and the full pool. Each mode has its own AI, trained separately by self-play — so the Expert opponents have actually learned to use these powers against you rather than following a script.