During Thor's coronation Odin gave a historical account of his responsibility as king and the responsibility of one to follow. In addition to that he also expressed the origin and value of Mjolnir. But he is quoted as saying "I have defended Asgard, and the lives of the innocent across the nine realms since the time of the great beginning." What did he actually mean by this?
Clearly there is no explanation for this in the MCU as the origin of the Nine Worlds is not covered in that medium. Equally, there is no direct explanation as to the "great beginning" of WHAT?
If we fall back on the comic book origins then, perhaps, Odin was referring to the origin of the Asgardian Realm (which is then divided in 9 other realms)
According to Asgardian legend, in the beginning there was nothing, but in time two worlds came into being on opposite sides of the void. The one to the north was named Niflheim, a world of clouds and shadows in whose center surged the fountain Hvergelmir, from which flowed twelve rivers of ice. The one to the south was named Muspelheim, which teemed with rivers of fire. Eventually the warm air from the south carved out the frost giant Ymir from the ice in the north.
Ymir became the father of all the giants, and his cow Auðumbla licked out of the ice the first Asgardian, Buri. Buri had a son named Borr, who married the giantess Bestla. Borr and Bestla had three sons named Odin, Vili, and Ve, who were known as the Æsir. Odin and his brothers grew to hate the giants and slew Ymir, and his blood formed a great sea.
Odin and his brothers then raised Ymir's body from the sea and created Midgard between Niflheim and Muspelheim. With Ymir's bones they created mountains, and with his hair they created trees. They then raised Ymir's skull upon four pillars to create the heavens. Within the skull contained sparks from Muspelheim, which became the sun, moon, and stars.
When Midgard was complete, Odin and his brothers created a home for themselves above it called Asgard.