TL;DR:- Approvals are required because Polynomial uses the Ethereum blockchain to settle transactions.
When using a Decentralized Application(dApp) like Polynomial, you must first approve each token you plan to deposit. Polynomial uses smart contracts on the Ethereum blockchain to execute transactions.
To use a smart contract, you must :
  • Permit it to validate your token balance
  • Let it transfer the number of tokens you wish to trade from your wallet.