Hot wallets are Bitcoin wallets that run on internet connected devices like a computer, mobile phone, or tablet. Private keys are secret codes that hot wallets generate on an internet connected device. As such we cannot say these private keys are completely secure.
Hot wallets are like your physical wallets which you use to store some cash, but not your life savings. Hot wallets are useful if you make frequent and small payments, but are not suitable to store a large amount of bitcoins.
Software wallets allow us to send and receive bitcoins and are mostly free. There are some paid software wallets which provide some extra value-added services.