What did Leslie suggest for her and Jess to have all to themselves?

The answer to this question is very important to the plot! Let's look in Chapter 4, titled "Rulers of Terabithia," when Leslie and Jess are playing together outside, near the creek bed:

"Do you know what we need?" Leslie called to him. Intoxicated as he was with the heavens, he couldn't imagine needing anything on earth.

"We need a place," she said, "just for us. It would be so secret that we would never tell anyone in the whole world about it." Jess came swinging back and dragged his feet to stop. She lowered her voice almost to a whisper. "It might be a whole secret country," she continued, "and you and I would be the rulers of it."

Leslie is saying that they should have their own secret imaginary country, outside somewhere, where just the two of them could hang out together, play, and come up with all kinds of adventures. They'll imagine that they're the rulers of this place, and it'll belong to them.

So you can imagine how the promise of this fascinating place stirs something within Jess! They walk a little further together and decide on a place to build their imaginary country. It's beautiful, the perfect spot to play this imaginative game together:

"...here where the dogwood and redwood played hide and seek between the oaks and evergreens, and the sun flung itself in golden streams through the trees to splash warmly at their feet."

Like you might guess from the title of this chapter, and from the title of the whole book, they name their secret kingdom "Terabithia."

When you consider how Jess often feels crowded at home with all those sisters, like he has no privacy, you can imagine how tantalizing the idea of a secret kingdom is to him. And, he's captivated by the idea of being in charge of something; he's always getting bossed around at home and, to some extent, at school also. Since he's already so fascinated by his new friend Leslie and her incredible imagination, we know that this Terabithia will become a special place for their friendship and for Jess's development as a person to unfold.