.INI files are Initilization files. They are used to store values outside of a programs EXE and then be read in at run time.
Initilization via this method provides many benefits along the lines of being able to change variables within a program without needing to recompile and redistribute the application.
Lets say you have a program that the user may choose to install to a location other than C:\ProgramFiles. Your installer would log the location to your INI file and then the program would still work because it loaded the value from the INI file. Had you hardcoded this path in the user would be unable to install the application to their chosen folder and have the program work.
All that being said, .INI files are technically the very old VB6 way of doing things. Microsofts reccomendation eventually went to using the registry (VB2003 IIRC) and now is that you use XML files to contain your initilization variables. (A very good suggestion, in my opinion)