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 that (e.g., texmf-dist, texmf-var).
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 /usr/share/texmf or /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.