Fiji is an image processing package. It can be described as a distribution of ImageJ together with Java, Java 3D and a lot of plugins organized into a coherent menu structure. Fiji compares to ImageJ as Ubuntu compares to Linux.
Fiji works with Bio-Formats out of the box, because it comes bundled with the Bio-Formats ImageJ plugins.
Upgrading Bio-Formats within Fiji is as simple as invoking the “Update Fiji” command from the Help menu. By default, Fiji even automatically checks for updates every time it is launched, so you will always be notified when new versions of Bio-Formats (or any other bundled plugin) are available.
Fiji currently ships with the latest 4.4.x Bio-Formats release. Alternately, you can enable the “Bio-Formats 5” update site to receive the latest Bio-Formats 5 bugfixes and updates.
For further details on Bio-Formats in Fiji, see the Bio-Formats Fiji wiki page.