What is the Fire Emblem?

I've only meaningfully played the Awakening (nearly finished but not yet) but I know there are many more titles out there. And from my past experience of skimming some of the other titles, it seems none of them are actually connected plot wise. However, all of these titles obviously have a Fire Emblem in it.

I already know that the Fire Emblem in Awakening is used in a ritual to summon the strength of the divine dragon.

But what about the other titles where the plot lines are different? What exactly does it do and are these games actually from the same universe? Or do they each have their own Fire Emblem that does something different.

I've searched for what the Fire Emblem is but all I got was articles introducing the series, not the particular artifact. What exactly is the Fire Emblem?

Thebluefish commented the link you want.

The "Fire Emblem" is the name given to each game's MacGuffin, though it is not necessarily the same object every time. It's always going to be an object of immense power, sought after by the enemy or protected by the protagonists, and often only the main hero can wield it properly.

To answer your other questions, all games in the series do take place in the same universe. Some are direct sequels (Path of Radiance to Radiant Dawn), some take place in the far future or past or on different continents, but they are all in the same world.