Yes, you are right; the depository can be compared with a bank, which holds the funds for depositors. The only difference is that a bank holds cash or funds on your behalf whereas the depository holds shares and other securities on your behalf. What exactly does a bank do for you? The bank holds funds in a bank account while the depository holds securities in an account. The bank permits transfer of funds from one account to another while a depository also permits transfer of shares from one account to another. The bank allows you to make interbank transfers and also intra-bank transfers of money. The depository allows you to make inter-depository transfers (NSDL to CDSL) and also to make intra-depository transfers (NSDL to NSDL) of shares. When you hold cash in your bank account, you can issue cheques against that to use the funds. When you hold shares in your demat account, you can issue a debit instruction slip (DIS) to make use of the shares in the account.
There are also some other interesting aspects. For example, the bank facilitates safekeeping of your cash whereas the depository facilitates safekeeping of your shares and other securities. What about dividends. When you hold shares in DP account, the dividends are automatically credited to your bank account that is mapped to the DP account. Even other corporate actions like rights, stock split shares, and bonus shares are all directly credited to your DP account. In a bank account, the interest is directly credited by the bank to your bank account. Both the DP account and the bank account are methods of maintaining your assets in a safe, secure and smart manner.