After running your system for a while and installing various tools, utilities, and other programs on your system, you may find two Applications folders on your system. The main one will hold most of your applications, but another one in your home directory may contain one or two applications you have installed. Despite this, the applications run fine and there seems to be no difference between the two folders.
The second Applications folder is created for the simple reason that an installer you ran created that directory and placed the application there. If this has occurred to you, you should be able to move the items from this directory into the main Applications folder (or reinstall the programs to the Applications folder) and then remove the folder from your home directory. However, before you do this there are a couple of benefits to having a personal Applications folder.
OS X is a multiuser environment that allows individual users to access globally shared items but then store user-specific items in a private location. In most cases private files are documents which are located in respective Documents, Movies, and Music folders, and are settings which are located in the user's Library folder.
In addition to documents and settings, users can also keep some applications private so only their account can have access to them. OS X recognizes this, and when you create a folder named "Applications" in your home directory the system will label it as an Applications folder just like the global one. With the programs in your home folder they will only be available to your account, so the system's launch services will not access them when other users are logged in. This will allow you to keep specific applications that only you find useful, and not clutter up other people's computing experience on the same computer.
As an example, if you are a text-editor junkie and want to try every text editor out there, you can install them all to the global Applications folder, but when another user tries to open a text document it may open in any of the text editors you installed. Since most users use TextEdit to modify text documents, you can install your own editor to your personal applications folder and use it to open text files, and other users will continue to use TextEdit without inadvertently opening the one in your account.
While useful in some instances and for some applications, this is a nonstandard way of running programs and some will not support being outside of the global Applications folder. I have found using a personal Applications folder is easiest for applications that install with a simple drag-and-drop.