Numbers
Numbers is part of iWork, an Apple application suite available as apps for OS-X and iOS as well as in a cloud-based version on iCloud. It is a spreadsheet program.
The web-based cloud version can be run in a browser (Not all browsers are fully supported; when you try it in Firefox, it says that it is an unsupported browser, but seems to work anyway, though it is possible some features aren't fully functional), and is free for iCloud users. The app version is paid, though apparently it comes free with newly-purchased iOS devices since late 2013; it will sync automatically with iCloud to access cloud-stored documents.
The current version can load and save the corresponding Microsoft Excel XLS file type (using, apparently, the 2003 file version). It can also save as PDF, producing a static document that can be useful for viewing, but not so much for editing or import into other software. And then there is the native iWork format, bearing a .numbers extension, or a double extension .numbers.zip when saved in a ZIP file.
iWork files, when saved under Mac OS-X, are in a bundle format that is actually a directory/folder. Saved in other systems, or exported as e-mail attachments, they are ZIPped and use the double extension as noted above.
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File format info
The basic file format is consistent across the iWork suite, and is documented more fully in the iWork article. In the 2013 version of the format, the different apps mostly differ in what IWA files are stored in the Index.zip file (a ZIP within the bundle).
Numbers (2013) files include DocumentStylesheet.iwa, ThemeStylesheet.iwa, Document.iwa, Metadata.iwa, CalculationEngine.iwa, and AnnotationAuthorStorage.iwa. The Tables subdirectory has DataList.iwa and a series of numbered files like DataList-1.iwa, DataList-2.iwa, and so on. There is also HeaderStorageBucket.iwa, HeaderStorageBucket-1.iwa, etc., and Tile-iwa, Tile-1.iwa, etc.
