What is "Pattichha Samuppadha" in buddhism

'Paṭicca+sam+uppāda' means 'dependent+co+origination'. It refers to 12 conditions that arise together to result in sorrow, lamentation, pain, grief & despair, as explained in the scripture SN 12.2.

It others words, it does not describe some conditions in the past, some conditions in the present & some conditions in the future and it is not about reincarnation or past and future lives. It is about 12 conditions that arise in the present that result in sorrow, lamentation, pain, grief & despair. The Buddha said about dependent co-origination:

Good, monks. You have been guided by me in this Dhamma which is to be seen here & now, immediate, inviting verification, pertinent, to be realized by the observant for themselves.

Mahatanhasankhaya Sutta

Anekajātisaṃsāraṃ sandhāvissaṃ anibbisaṃ gahakārakaṃ gavesanto dukkhājātipunappunaṃ is about the mind cycling/spinning in "births". The word "birth" ("jati") means "identity", which is a fixed view of self or "beings" ("satta") born from attachment & craving. The "builder of the house" ("gahakārakaṃ") is craving; is all twelve conditions of dependent origination.

Therefore, in terms of Dependent Origination, "identity" ("birth") means things attached to called "acquisitions" ("upadhi"), as follows:

And what may be said to be subject to birth? Spouses & children are subject to birth. Men & women slaves... goats & sheep... fowl & pigs... elephants, cattle, horses, & mares... gold & silver are subject to birth. Subject to birth are these acquisitions, and one who is tied to them, infatuated with them, who has totally fallen for them, being subject to birth, seeks what is likewise subject to birth.

Ariyapariyesana Sutta

"Identity" includes attachments such as "myself", "my life", "my mother", "my father", "my sister", "my daughter", "my brother", "my son", "my friend", "my car", "my computer", "my money", etc.

When these attachments are lost because of impermanence, the idea of "death" arises, such as the "death of my mother", "death of my father", "death of my son", "death of myself".

Because of this "death", there is sorrow, lamentation, pain, grief & despair and suffering.

Therefore, when Buddha destroyed the house-builder of craving & dependent origination, the Buddha also destroyed "identity" or "self". When there is no "identity", there is no "death" and no suffering.

The scriptures say:

Bhikkhu, ‘I am’ is a conceiving; ‘I am this’ is a conceiving; ‘I shall be’ is a conceiving; ‘I shall not be’ is a conceiving; ‘I shall be possessed of form’ is a conceiving; ‘I shall be formless’ is a conceiving; ‘I shall be percipient’ is a conceiving; ‘I shall be non-percipient’ is a conceiving; ‘I shall be neither-percipient-nor-non-percipient’ is a conceiving. Conceiving is a disease, conceiving is a tumour, conceiving is a dart. By overcoming all conceivings, bhikkhu, one is called a sage at peace. And the sage at peace is not born, does not age, does not die; he is not shaken and does not yearn. For there is nothing present in him by which he might be born. Not being born, how could he age? Not ageing, how could he die? Not dying, how could he be shaken? Not being shaken, why should he yearn?

Dhatu-vibhanga Sutta

Pratityasamutpada means "gradual auto-emerging". It describes the process by which a newborn baby develops subjective experience of "I" and "desirable/undesirable objects" and "the world".

Information is an ever-present part of the universe. All physical interactions carry information. As these interactions have some amount of regularity (they repeat in patterns) - the baby accumulates information.

As information accumulates, it becomes more and more complex and integrated, until it can reflect or represent something about the world. Now it can be called "mind".

This process evolves until it culminates in recognition, when the baby can recognize something from before, and associations when it can relate things that were somehow connected before.

The process evolves further until the baby develops notions of objects or entities, each having a stable identity. The baby begins classifying these objects as "desirable" and "undesirable" based on experience of peace or disturbance that they bring. It starts pursuing desirable objects and avoiding undesirable.

Then gradually the baby develops a notion of "I", as the subject that experiences contact with the objects, and as the entity that pursues an object and enjoys the result.

In the baby's mind there is entire world, with people, objects, problems, and happy moments. It grows, matures, gets old, and dies.

Then the cycle restarts when a new baby is born. It starts from scratch again, going through the same process. This goes on indefinitely.

Every generation starts with complete ignorance of the fact that nothing completely disappears and nothing appears from scratch, and that everything keeps transforming from one form to another. Every person grows up assuming that he or she is completely separate from everyone and everything else. Then they begin pursuing some selfish goals and fighting with each other. The cycle repeats on and on.

If only they knew that this world of separation is an illusion! They would teach their children to live differently! No pursuit of stupid material goals, no fear of death, no fighting, no murdering the planet! But they don't know and so the cycle goes on and on and on...

This is "the cycle of existence" that "has run through numerous births".

Thus, this twelvefold dependent arising — which comes from several different causes and conditions, is neither permanent nor impermanent, is neither compounded nor uncompounded, is not without cause or condition, is not an experiencer, and is not something exhaustible, something destructible, or something that ceases — has proceeded from time immemorial, without interruption, like the flow of a river. - The Rice Seedling Sutra.

Now, if you look at this process from afar, you will see that it's not really about an individual baby, it is about the overall pattern of subjective experience emerging from information and then taking its model of reality for reality itself. The exact way this happens, the reason it relates to Buddhist Ethics, and the way to undo it, is the heart of hearts of Buddhism.