These are software apps available on mobile phones, desktops, laptops or websites that allow bitcoin transactions.
For those people who use Bitcoins frequently, paying for goods and services, a mobile bitcoin wallet is a necessary tool. A mobile app runs on your smartphone, has your private keys and allows making payments directly from your phone.
A full Bitcoin client would require access to the complete Blockchain ledger, which needs several gigabytes of storage. Therefore, mobile wallets use simplified payment verification (SPV) technology which works with very small subsets of the Blockchain. In spite of being a convenient on-the-go solution for Bitcoin transactions, mobile wallets are very susceptible to hacker attacks and also if the mobile is lost, others can access the wallet.