Tagged means extensible
A TIFF is a directory of tags, each declaring one property of the image: dimensions, bit depth, compression method, colour space, resolution, orientation, and dozens more. A reader walks the tags and interprets what it finds. That design is why TIFF absorbed 40 years of change without breaking — new capabilities simply became new tags.
It is also the source of TIFF's reputation for inconsistency. The specification permits so many combinations that no reader implements all of them, so a valid TIFF written by one program can genuinely be unreadable by another. Files using unusual compression, exotic colour spaces, or floating-point samples are the usual offenders.
Why archives and scanners chose it
TIFF can be fully lossless while storing more colour depth than any consumer format needs — 16 bits per channel is routine, which matters when an image will be adjusted repeatedly and you want headroom before banding appears. It handles CMYK and Lab natively, so it survives a print workflow without a colour conversion.
The multipage capability is the other half of the story. A scanned twenty-page document can be one TIFF file with twenty images inside, which is exactly what document scanners and fax systems need — and CCITT Group 4 compression makes bitonal scanned text remarkably compact.
Why your browser will not show it
No mainstream browser except Safari displays TIFF, and support was never added because the format is large, complex, and aimed at production rather than delivery. Emailing a TIFF or putting one on a website therefore does not work — it downloads rather than displaying.
For distribution, convert: JPG for photographic content going to the web, PNG when it needs to stay lossless, and PDF for multipage scanned documents, which is what most people actually want when they have a multipage TIFF in hand.
Converting TIFF files
Converting TIFF to JPG is the standard step for sharing photographic scans. It is lossy, so keep the TIFF as the master — that is the whole reason you have one. Converting to PNG stays lossless and preserves transparency, but 16-bit-per-channel TIFFs will be reduced to 8 bits, which loses editing headroom you may care about.
Be aware that a browser-based converter reads the first image in a multipage TIFF. For a multipage document, a PDF conversion that keeps every page is what you actually want.