If you are trying to upgrade to a new version of DF and keep your saved games, then you need to perform several steps.
1) Your existing DF directory should be renamed. (I like to rename mine from df_linux to df_linux_3410 or whatever.)
2) After extracting the new version of DF, consider renaming the new directory, to avoid accidents.... Do not extract a new version of DF into an old version's directory.
2.5) Edit the data/init/init.txt and data/init/d_init.txt files in the new version. Don't copy the old version's init files over, as there may have been other changes that you'd lose.
3) Create the data/save/ subdirectory inside the new version, since that isn't created when you extract the tarball.
4) Copy (recursively, e.g. with cp -a) the data/save/regionN/ subdirectory (which is your saved game/world) from the old DF version to the new DF version.
5) If there were changes to the raw files between the two versions, and if those changes may be safely applied to an old fortress without crashing (depends on the changes!), then you must edit the data/save/regionN/raw/* files accordingly. Otherwise the existing save will continue to use its original raw files.
If you aren't on Linux, adjust the instructions for whatever platform you're on.
When in doubt, it's best to generate a new world.