TDS stands for the TeX Directory Structure, which is a standard way of organising all the TeX-related files on a computer system.
Most modern distributions conform to the TDS, which
provides for both a 'standard' hierarchy and a 'local' hierarchy. The
TDS reserves the name texmf as the name of the root directory
(folder) of the hierarchies. Files supplied as part of the
distribution are put into the standard hierarchy. The location of the
standard hierarchy is system dependent, but on a Unix system it might
be at
/usr/local/texmf, or
/usr/local/share/texmf, or
/opt/texmf, or
a similar location, but in each case the TeX files will be under the
/texmf subdirectory.
There can be multiple 'local' hierarchies in which additional files can be put. In the extreme an installation can have a local hierarchy and each user can also have an individual local hierarchy. The location of any local hierarchy is not only system dependent but also user dependent. Again, though, all files should be put under a local /texmf directory.