I am still in the middle of Season 1 of Vikings, so its very well possible that this is a plot point being explained later. Maybe I just missed it.
From the start, I always assumed that Bjorn was Ragnar's biological son. He certainly raises him like one and I recall them calling each other son and father respectively.
However, Ragnar is extremely happy when his wife Lagertha tells him that she is pregnant, saying that he is sure that it will be a son.
When the unborn child dies, Ragnar is afraid that "he will never have a son" and it becomes apparent that he and Lagertha already tried many times without success to have another (?) son.
What is going on? I can understand why Ragnar would want a son so desperately (as a successor), but what doesn't he have one already? Also why do Ragnar and Lagertha keep talking like they have not been able to have a son yet?
In the temple in Upsala Lagertha prays to Odin:
Do as you will with me, make me blind or death if you want. But give me a son...before it's too late!
Is Bjorn not Ragnar's son? Or is he from another woman? Why would that matter?