With the exception of the European Union member states, where you can load Apps from alternative App Stores, Apps can only be downloaded and installed from Apple's App Store.
Otherwise, assuming that you have not jailbroken your iPhone (such action being strongly ill-advised), the only other method outside of Enterprise and Educational environments where devices are centrally managed is to install a developer profile. If you are not a developer creating your own Apps, this becomes an exercise in trust - as you will potentially expose all your personal, sensitive and private data to an unknown third-party.
As such, unless you have explicit trust in the Developer and their motives, you would be well advised to steer well clear. Apple devices are designed to have very robust security - but this premise relies upon only installing software that has been vetted by Apple's review processes. While these processes are not infallible, they do provide a high degree of confidence that your data and privacy will be preserved. If you venture into mechanisms to bypass these protections, you invite the possibility of giving access to sensitive material, fraud or financial loss.
If you cannot provide adequate assurance that you proposed use of Apps or software from an untrusted source is safe, you court unexpected consequences and outcome.