To reveal a card is to show the card's face to all players.
After revealing the cards, they normally return to their original position. Revealing the card does not activate it, nor does it activate or apply its effect. Revealing a face-down card does not count as flipping it.
If a card is already public knowledge, it cannot be revealed. For example, if "Mind on Air" is face up on a player's side of the field (with its effect active), their opponent cannot activate the effect of "Golden Ladybug".
Reveal for verification
Sometimes cards must be revealed to prevent cheating.
When an effect causes a player to search for a card of a specific type in their Deck, that player must reveal the card to their opponent before adding it to their hand, Setting it on the field or placing it on the top of the Deck with that effect. For example, when a player adds a Monster Card to their hand using the effect of "Sangan", their opponent may read all of the information on the Monster Card added.
If a mandatory effect would search for a card(s) but no cards in the Deck meet the required criteria, then that player's Deck must be revealed to their opponent. For example, when a player activates "Magician's Circle" and their opponent has no card that meets the required criteria in their Main Deck, they must reveal their Main Deck to prove that they cannot Special Summon a monster.
While resolving an effect that asks for a card to be verified, if all legal copies of that specific card can be accounted for in public knowledge areas, the area that would be revealed does not need to be. For example, if a player uses "Mind Crush" and names a Limited card, and it is public knowledge that the opponent's only legal copy of that card is not in their hand (e.g. it is in the Graveyard), their hand does not need to be revealed.
In the case where an effect requires the hand to be revealed, the opponent may read every card in the hand. For example, if a player uses "Trap Dustshoot", they may look at all the cards in their opponent's hand, even the non-Monster Cards.