When moving funds from Mainnet (L1) to Arbitrum (L2), you'll need ETH in your Arbitrum wallet.
Even if you want only to use another, non-ETH, token, you will still need a small amount of ETH in your wallet on the Arbitrum network. This is because all Arbitrum transactions are powered by ETH.
ETH is the currency used for gas fees. Arbitrum gas fees go to Arbitrum validators to track chain state and execute transactions. This is actually an estimated fee; if the true fee is lower, then you will be refunded.