An .ini file is a standard file and is not something that is special to LabVIEW. LabVIEW itself uses an .ini file to store some application settings that you change via the Tools->Options menu. It is not wise to change this file yourself manually. You can create your own .ini files for your application. You can use the VIs in the Configration File VIs palette to read/write .ini files. This palette is a sub-palette from the File I/O palette.
As for its format, it's made up of sections and keys like this:
[Section1]
keyname=value
keyname=value
[Section2]
keyname=value
;this is a comment
If the value you're trying to save is a string you should use quotes.
What you store in the .ini file is up to you and how you use it is also up to you. You can access the keys on an as-needed basis, or you can read the keys in at the beginning of your program, store them someplace like a global variable and access them as needed. It's kind of dependent on the size and architecture of your application.