The Tiger hash function was invented by Eli Biham and Ross Anderson. It is significantly different in internal structure from most other hash functions in use (such as MD5 and SHA-1), making use of multiplications and substitution boxes rather than lots of interleaved additions and bit-logical operations, which is the method used by most other hash functions.
It produces a 192-bit output, and internally uses 64-bit integer arithmetic. The multiplications are done against constant values: 5, 7, and 9 (the DEC (see also Compaq) Alpha has special instructions for these multiplications, which was why those specific values were chosen). The mutiplications are used to spread out the bits; a single bit change in the input will affect many of the bits of the output (the term for this is high diffusion).
So far, there are no known attacks, but nobody is using it much either (in that sense it is pretty similiar to the HAVAL hash function). The only place it is being used in (to my knowledge) is in the IETF OpenPGP standard as an optional algorithm; GnuPG actually implements it.
It seems Biham and Anderson like using animal names for cryptographic primitives: they have worked on Tiger, Serpent (with Lars Knudsen), Lion, Bear, Lioness, and Chameleon.