Bitcoins are really just account balances stored in a large, shared, global ledger. As long as you can connect to that ledger and prove ownership of your account, you can spend its balance, regardless of if you access that ledger with a phone app, a computer program, or a browser.
The thing that proves that you own the account is the «private key» that is used to sign the transactions you make, and that is what is typically stored in bitcoin wallet apps.
Some bitcoin wallet and web apps store that key on the wallet company’s servers for you, meaning the company could get full access to you bitcoin account if they wanted to. However, with Mycelium Bitcoin Wallet, your private keys are stored on your phone, and they never leave your device unless you make a backup. The developers of the Mycelium Bitcoin Wallet have no access to your private keys and therefore you are in complete control of your funds.
Although this provides you with full control and ownership of your bitcoins, it also means that you are completely responsible with what happens to your coins and your private keys. Therefore it is important that you make a backup of your wallet, and store it in a safe secure place, as well as keep your phone safe, or at least enable the PIN security on your wallet.
If you have not made a backup and you lose your phone or uninstall the Mycelium Bitcoin Wallet, your bitcoins will be lost forever.