A PDF is a static e-book format with fixed pages (citable) and a layout that can be opened on PCs, tablets, smartphones and most e-readers.
The text of an EPUB is dynamically adapted to the e-reader when you change the font size or the font, for example. EPUBs can be opened by all available e-readers (except for readers of the Amazon Kindle family), e.g. Tolino, Kobo, Sony Reader. The format is also particularly suitable for smaller devices, such as, for example, smartphones.
The MOBI format is a special e-book format for Amazon Kindle devices. Like the EPUB, it dynamically adapts to the reader.
You can also read EPUB and MOBI files on your PC or tablet (e.g. Adobe Digital Edition, Kindle app) with different programs.