Your Address can also be known as you Account # or your Public Key. It is what you share with people so they can send you DASH. Since the DASH blockchain is public and open, you can check any address (yours or any other) via the Public Key.
Unlike Unlock Wallet you won't need to access your hardware wallet or stored private key here. As long as you know your (or any other) address, you can always check whats going on via https://MyDashWallet.org:3001/insight/. If your unlocked your wallet before your last used wallet address is shown here automatically, but you can enter any other address just as well.
Enter Wallet Address to check; it looks like this: XoASepVfo1cegWp52HS9gbcKuarLyqxsKT