A good place to see a display of lachrymose sorrow is at a funeral — people sobbing openly or sniffling quietly into their hankies. To be lachrymose, in other words, is to be tearful.
Lachrymose is not a word used much in everyday speech; you wouldn't say, for example, "I feel a bit lachrymose today." No, you'd probably say, "I feel a bit weepy today." Lachrymose is generally confined to use as a written critical term, often meaning much the same as sentimental. Books and plays and films can all be lachrymose, if their intent is to induce shameless sniveling.