TDS is an acronym for “TeX Directory Structure”; it specifies a standard way of organising all the TeX-related files on a computer system.
Most modern distributions arrange their TeX files in conformance
with the TDS, using both a “distribution” directory tree and a
(set of) “local” directory trees, each containing TeX-related
files. The TDS recommends the name
texmf for the name
of the root directory (folder) of an hierarchy; in practice there are
typically several such trees, each of which has a name that compounds
Files supplied as part of the distribution are put into the
distribution's tree, but the location of the distribution's hierarchy is
system dependent. (On a Unix system it might be at
/opt/texmf, or a similar location.)
There may be more than one “local” hierarchy in which additional files can be stored. An installation will also typically offer a local hierarchy, while each user may have an individual local hierarchy.
The TDS itself is published as the output of a TUG Technical Working Group. You may browse an on-line version of the standard, and copies in several other formats (including source) are available on CTAN.