A Bitcoin wallet is a software program where Bitcoins are stored. To be technically accurate, Bitcoins are not stored anywhere; there is a private key (secret number) for every Bitcoin address that is saved in the Bitcoin wallet of the person who owns the balance.
You can download a variety of different Bitcoin wallets for free from the Apple app store or Google play store to your mobile phone.
Some of the more popular wallets are Jaxx, Blockchain.info, Coinomi.
If you are a first time user we recommend we recommend Zengo.
For hardcore Ethereum users our recommendation is Argent.