A custodian account is one where your brokerage acts as your custodian. The stocks are purchased through a nominee account that is managed by the brokerage firm. This means that the owner of the stock is legally the brokerage house and they hold the stocks on your behalf.
A custodian account is required in order for you to buy and sell the shares in overseas markets. You can also opt to use a custodian account when trading stocks on the Singapore market.