LastPass is a company that is on a mission to ensure that no one has to remember more passwords than absolutely necessary. A desktop version of the program is available, and this can be used to store all of your passwords and important information in one handy, secure location.
The iPhone and iPad version of the program enables you to access the information you have already associated with your LastPass account, or to create a new one. This means that you can access your passwords from any computer or device.
The integrated browser can be used to surf the web, and when you are shopping online, you can take advantage of LastPass' form filler to quickly fill in common field such as addresses.
It is unfortunate that LastPass cannot be used in conjunction with Safari, but this is one of the limitation of the idevice platform. There is the option of using a bookmarklet to access some of the features of the program, and while this is a far from perfect solution, it is the best that is currently available - and you'll probably be more than happy to stick with using the main app anyway.