What are all the start game conversations made in Overwatch? [closed]

They are called "interactions" and it's the way the game explains in a very brief way the story behind your selected character and the one your character is interacting with.

A good example would be Sombra, you can see all of Sombra's interactions here, you can see in those interactions Widowmaker's contempt towards Sombra because of the failed mission to kill Katya Volskaya they had alongside Reaper. You can also see how several other characters are not precisely happy with her about something.

That's exactly what those small conversations mean, they are ways to show you a bit about the story between those characters interacting.

Here you can select one of the heroes and then click on the quotation page to see every voice line they have, including the interactions.

Adding an image since the link is kind of elusive: