Independent Films are normally not directly funded by the major studios.
Worldwide there are thousands of small independent Companies.
Below are some prominent companies of which a fair number are subsidiaries of the major companies.
Lions Gate
Fox Searchlight Pictures
Focus Features/Rogue Pictures
Sony Pictures Classics
IFC
Samuel Goldwyn
Warner Independent Pictures
The Weinstein Company/Dimension
Magnolia Pictures
Paramount Vantage
Palm Pictures
Tartan
Newmarket
Picturehouse
ThinkFilm
Miramax
Troma Entertainment
These companies don't normally have the distribution resources for showing in theaters which is controlled by the major companies so successful distribution is challenging.
With the development of very high quality but inexpensive cameras, more and more projects are being produced independently from the major studios.
Many are submitted to festivals to get exposure in the hopes of being picked up by one of the major studios.