I agree with Paul. Some British people, particularly from London, would understand it, but it's probably falling out of use.
It's interesting that this word isn't known in the USA. In general, Yiddish words are much more prevalent in mainstream US English than they are in British English. Terms such as 'kvetsch' (meaning complain), 'schmuck' (meaning an idiot) and 'chutzpah' (meaning audacity) are familiar to most Americans, but far less so to British people. 'Schtum' seems to be the exception in this case.
One explanation for this anomaly is that the expression may not be Yiddish at all, but a London English word derived directly from German. Apparently, the first record of this was in the 1950s, long after the heyday of the Yiddish language. It emerged in London's criminal underworld, and meant keeping one's mouth shut and not 'grassing' (i.e. 'snitching) on fellow criminals.
As for your question, Rafaela, which, incidentally, should be 'When should I use "Keep Schtum" ?' ('When to use..?' sounds like pidgin English), the answer is probably 'never'. It's a low-frequency, dialect term, which you will most likely never come across again.