I have a cyst on my ovary and is causing me pain- gynaecologist spoke about operation but is now saying to leave it and rest. is this right?

It is: It depends on how long the pain has been going on and how severe it is, but generally there is no benefit to removing an ovarian cyst because the vast majority of them go away either by rupturing (which is painful but not dangerous) or just regressing. In fact, it's normal to have cysts on ovaries unless they get too big, too numerous, bleed or cause long-lasting symptoms. Ibuprofen often helps.