AI is a source, fully editable vector-based file format. You can open and edit .ai files in Adobe Illustrator.
EPS (Encapsulated PostScript) is a vector file format that is most commonly used for high-resolution printing. You can open and edit .eps files in Adobe Illustrator or Adobe InDesign.
JPEG (also known as JPG) is a very popular compressed file format used for storing and sharing graphic elements and photos. You can open .jpg files in almost any software that supports image editing.
PNG (Portable Network Graphics) is a raster graphics file format used for storing and sharing line drawings, icons and symbols. Unlike .jpg, it is a lossless format that allows compressing images without quality loss. Files with .png extension can have transparent backgrounds which makes it easy to place the artwork on different backgrounds. Most of the image-editing programs support .png.
SVG (Scalable Vector Graphics) is a vector image format specifically developed for the use in the web. Just like AI and EPS files, artwork saved in SVG can be infinitely scaled to a larger size without quality loss. All the major modern browsers support this file format. You can open and edit .svg files in most Adobe software products.