Question: why do we celebrate birthdays of people that arent alive anymore? i mean tzaddikim , rabbis etc. how does it work and why?

Shalom, Thank you for your question. In mainstream normative Jewish practice birthdays, even of people who are alive, do not have any special significance. Socially, they are a chance for people to mark milestones in their life, and for others to celebrate with them the blessings of another year. However, religiously, we do not find any particular importance to a birthday. (Attaining a certain age sometimes does have religious meaning – such as bar and bat mitzvah. But this is due to reaching the age, not due to any specialness in the birthday itself). Some (mainly Chabad chassidim) make a point of using a birthday as a means to strengthen oneself religiously. This is a worthy practice – but by no means obligatory or even widespread in the Orthodox world. Now to your question of the importance of the birthday of tzadikim who are dead. In general, here too there is no particular importance to the birthday. However, it may be used as a chance to recall the righteous individual to mind, and help us learn from them. According to Chassidic kabalistic thought the day itself may have some religious meaning. But, this is not a widespread belief. In general religious Jews mark the anniversary of the death of a Jew – the “yartziet” as the correct time to pray and help elevate the soul in the next world. Blessings.