In the game, there are 3 different signs. They are Rock, Paper and Scissors. If you choose the stronger sign, you win the battle against the opposing dinosaur and attack them, lowering their life gauge. However, your own life gauge will lower if they choose the stronger sign or if there is a tie, in which both players' life gagues are lowered. This continues until one player's life gague is empty.
Rock
Rock beats Scissors, but loses to Paper. When you win with this sign, your dinosaur swings around and knocks over your opponent with its tail.
Paper
Paper beats Rock, but loses to Scissors. When you win with this sign, your dinosaur flips your opponent up, and they land a distance away.
Scissors
Scissors beats Paper, but loses to Rock. When you win with this sign, your dinosaur rushes forward, smashing into your opponent, sending skidding a distance away.
Arcade Usage
All arcade Dinosaurs and Moves have a corresponding Rock-Paper-Scissors sign.
All dinosaurs have an Attack stat for each of the three signs (not the Power stat, and only visible on certain card versions). Two of them are typically equal, and the third one is the highest—this corresponds to the sign of the dinosaur, and is called that dinosaur's "critical move".
Move Card signs correspond to which ones can be used. During an arcade battle, your dinosaur can only have access to a maximum of 3 Moves, and each one has to have a different Rock-Paper-Scissors sign regardless of how many are used. Secret Moves, although they don't have separate cards, also have signs. To use them, simply swipe a Super Move of any element when using a Secret Dinosaur, and you gain access to its Secret Move with the corresponding sign. Ultimate Moves (any "built-in" Moves that can only be used by a dinosaur in their armored form) have no sign.
TCG Usage
All TCG Dinosaurs have signs. When one attacks another, their signs are compared. Whichever one is losing has the chance to use a Move Card first (they don't have to, but this is their only chance), then the one that won can use a Move Card (they don't have to, but this is their only chance). The advantage to winning at Rock-Paper-Scissors is that you know whether or not you need to use a Move (if there's no way you can win, you don't have to waste a card).
Very few TCG Moves have signs, and no Normal Moves do. Those Move Cards that do have signs (only Super Moves) can only be used by a Dinosaur of the same element and sign.