They were used to announce births, deaths and also as greeting on a wedding. There was a whole array of emotions aligned with telegrams. We have sent plenty of them: greeting relatives on their wedding, births, birthdays and anniversaries. We have also received numerous ones announcing death of a loved one. You could write ten addresses and send one message to all ten, as happened during a bereavement of a family member. The postman who delivered these telegrams at an odd hour with a solemn face was called "Maranam" and we used to whisper as he came towards our house "Maranam vannu (death has arrived)". During our sister's wedding a bunch of telegrams were delivered with the standard message "May heavens shower choicest blessings on the newly wed couple". Cute. This standard message was associated with a number and one only had to write the number for the receiving post office to write the greeting by hand.
BSNL has announced they are stopping telegrams from July 1, according to this report in Hindu.
So, those were the days, we can say in retrospect now. It's like an age has passed, a zeitgeist has ended, and an institution has died.
And, while saying adieu to this too-difficult-to-say-goodbye article of daily life (shedding copious tears), this picture alongside is what a telegram sent from Bombay to Karachi looked like.