TIFF (aka .tif or .tiff files), or Tagged Image File Format, is generally used for high-quality storage, especially of scanned images. Since it's generally used as a lossless format without compression (or with lossless compression), it's not looked upon favorably as a format for publishing images to the web. Bigger file sizes of TIFF files = longer download times. You would be better off converting the image to JPEG, GIF, or PNG. Given the image in question is photographic, a high-quality JPEG is probably your best bet.
Presumably because it's a file format used primarily for storage and editing, not for online distribution, it is generally NOT supported in web browsers.
Safari seems to be the only mainstream browser that supports it natively. Others might be able to display it by plugin, but you probably can't rely on users having the right plugin.
Best course of action: convert to high quality JPEG.