The Circle of Life is such a big symbolic deal in The Lion King that it actually gets its own song:

It's the Circle of Life
And it moves us all
Through despair and hope
Through faith and love
Till we find our place
On the path unwinding
In the Circle
The Circle of Life.

The Circle of Life isn't a concrete thing you can point to or look at. Rather, it's a symbolic term for the series of events that unfolds on earth, bringing us from cradle to grave, through ups and downs, love and misfortune, and so on.

It also refers to how events tend to repeat themselves: Simba grows up, learns about manhood, and becomes the Lion King—and then he has a son who in turn will grow up, learn about manhood, and become the Lion King.

The Circle of Life is greater than all of us, and yet we're all connected to it. (Pretty trippy, huh?) From the smallest ant to the largest antelope, we're all just living in this world and trying to make our own way. The opening sequence makes this super clear for even the most casual viewer of the film: we see animals of all shapes and sizes traveling to Simba's presentation. Although they're all extremely different, these animals exist together in a peaceful and beautiful harmony that mirrors the Circle of Life itself.

This also ties in neatly with many of the themes of spirituality and interspecies inter-connectedness in The Lion King: Mufasa's opening lecture to Simba speaks to the power of the Circle of Life very eloquently:

"When we die, our bodies become the grass. And the antelope eat the grass. And so we are all connected in the great Circle of Life."

Whoaaa. That's deep.