Samudra manthan can translate to "churning of the ocean".
Both the devtas and the asurs want to churn the amrit (the nectar of immortality) from the deep waters of the ocean into which it has descended.
To do this, they must work together. They approach it as an Indian wife in the gaon might use a spinning churn to bring the butter from the milk - but because the job is such a large one, it is a mountain (Mandara) that serves as the pivot and Vasuki, the great nagraj, who serves as the rope. Vishnuji takes the kurmavatar (turtle avatar) to support the mountain on his back, so that it does not sink beneath the waves.
Many things are at that point concealed in the deep waters - in some versions of the story, the two teams working together churn up Kamdhenu (the cow which grants desires), Airavat (Indras elephant), many jewels of great beauty and power, etc. But the most wonderful thing they churn out is Sri - the wealth and fortune-bringing goddess Lakshmi. (That is why she had left Vaikunth and Vishnuji in the serial - she had gone to ocean) But, of course, there is always bitter with sweet, and so...in their quest to churn out the amrit, the prize they seek, they first cause the halahal vrish - the terrible poison - to emerge.
This poison has the potential to harm the whole world - it is as if all the evils are present in it. No one knows what to do as all are beginning to feel its effects and none can contain it. Only Shivji - who stands apart from sansar and is all powerful - he is able to handle all types of poison.
The devtas and asurs all begin to hymn to Shivji to please come and help them. Mahadev arrives and drinks the poison, keeping it in his throat. It is powerful and colors his throat blue, but does not harm him as he is more powerful still. His blue throat is the cause of his name, "Neelkanth".
After Shivji has saved everyone, they are able to continue the churning and eventually they discover the amrit. The asurs are quick to grab it for themselves and run off - which leads to Vishnuji taking his Mohini form to entice the asurs. He tricks them thus and gets the amrit only to the devtas. Hence, devtas are immortal, but asurs can be killed. (Except one - you will see what he does in the serial! He is Rahu-Ketu)
This is much shortened version of the story, but I hope it has helped!😊