Before now, you thought RSVP meant Rice Stew Very Plenty. Right? Far from it. RSVP is the shortened form of the French phrase, 'Répondez S'il Vous Plait' which means 'please reply'.
When this abbreviation is written in an invitation, it means that the organisers would like you to confirm that you would attend the event. Invitees may also be required to confirm attendance by a specified time.
For example, when an invitation reads, 'RSVP by 30th of January, 2020', invitees are expected to send a positive response, on or before the specified date.
Some event organisers take this seriously and make plans based on feedback. They may interpret your silence as being rude or as a rejection or they could just assume that you are undecided. Meanwhile, other people just write 'RSVP' as a mere formality.
In any case, it's a good idea for invitees to communicate their response to the organisers. Organisers could also send reminders.