Files with .odt suffix (entire name is OpenDocument Text) is part of open file format created for office applications. It is based on XML, this file type has very good stylization and font changing. It can be used in many ways, for example note taking application from your school because of its stability. It has fluent control. This file format serves for opening files created for example in OpenOffice.org Writer. It is default format for this program. This program belongs to OpenOffice.org family, which is now divided into Apache Office and LibreOffice. His first version was released on 1. May, 2005 and its latest version was created in September 2011.
Another program used for opening and editing these files is Microsoft Office Word. Several years ago, compatibility between Microsoft Office Word and ODT file format wasn´t very good. Sometimes there were mistakes in text, for example confusion of characters, another font type, etc. In recent years compatibility was repaired and there are almost no more mistakes in text transferring. Last possible programs for using this file format are Google Docs or Microsoft Word Online applications.
There is similar file format, which is called .docx usually used by Microsoft Office Word. For their comparison we can use statistics from Microsoft web. Transfer between these two file formats is not always very smooth. Not always is .odt file type supporting functions from .docx file types, for example .odt is not supporting encryption, there is limited number of tables, etc.
But, the main plus is, that this format can be used for free, no one will charge you for using it. It was developed by public and is still updated. In every possible way, .odt is awesome replacement for .docx file format.