All three ninja grew up in Konoha, and were all apart of the same team when they were Genin. The team's leader was Hiruzen Sarutobi. Hiruzen was the Hokage when the series was introduced, and was a major supporter of Naruto and his dreams of becoming Hokage. So all three of the students weren't called the Sannin at the time, that would come later in there lives. However, all three showed impressive skills and talent of the ninja arts that no doubt gave Hiruzen a foreshadow of the power they would have one day.
Later in their lives, they would fight in the Second Shinobi World War, where they faught Hanzo. Becuase he was so powerful at the time, it was difficult for any one person or army to stop him, and just three ninja's were able to challenge his power. Becuase of this, he called them Konoha's Sannin, though they are just known as the Sannin for short. That is when Jiraiya met Nagato, Konan, and Yahiko. The Sannin had mixed opinions about what to do with the children, but Jiraiya eventually came to stay with them and train them, not knowing of the destruction they would cause one day.
All three used their respected summons, Orochimaru with Manda, Jiraiya with Gamabunta, and Tsunade with Katsuyu. Showing all their affinities with their respected animal, also tying into the old Chinese folklore of the Slug fearing the Toad, the Toad fearing the Snake, and the Snake fearing the Slug. This is most often presumed to show that they are more or less equal in power, but in different areas may excel than each other. Its also interesting to note that each of Team 7 have trained with one of the Sannin. Naruto trained with Jiraiya, Sakura trained with Tsunade, and Sasuke trained with Orochimaru at some point. Each bringing back abilities and traits that model their respective mentors.
So that is my basic run-up of the Sannin, their isn't a whole lot of time spent on them, but I covered the major appearences of them. Note that I didn't use this blog to specify each member, but the activity when all three were together.
Hope you enjoyed !