What is an ODF file?
VoidSoul
An ODF file is a document created by Apache OpenOffice Math, a program used for creating math formulas. It contains one or more mathematical equations and may also contain macros. ODF files are based on the OASIS OpenDocument standard.

ODF file open in OpenOffice Math 4.1.3
The ODF file is the main file type used by Math to save equations. The file is most commonly opened in Math to create or edit formulas but may also be imported into other applications, particularly OpenOffice programs such as Calc or Impress. When it is imported into another application, the equation functions like an object that can be placed in a research paper, presentation, etc.
Math allows you to enter formulas in an ODF file three different ways. You can add markup in the equation editor, select a symbol from the "Elements" toolbox, or right-click the equation editor and select a symbol in the context menu. When you are done with your equation you can share it via email or export it as a .PDF file.
NOTE: Apache OpenOffice was formerly known as OpenOffice.org.