The answer to your question can be found in chapter 13. After trying unsuccessfully to find the paints that he had discarded near Terabithia the day before in his immense grief over Leslie's death, Jesse enters Terabithia, wondering if it will still be a magical place.

Jess feels that he wants to "do something fitting" to honor Leslie in the place that had been so special to both of them. However, he doesn't know what to do, and since Leslie isn't there to tell him, he starts to feel angry again.

On his first visit to Terabithia without Leslie, Jesse thinks about her death, and wonders whether she was scared when she fell. He then realizes what he would like to do for "the queen," and informs PT that they "must make a funeral wreath." He starts out by bending a pine bough until it is round, and tying it in place. He then adds "spring beauties" to the wreath.

He then places the wreath "into the dark center of the grove" and prays, knowing that Leslie would have liked the religious sentiment. In many cultures around the world, a funeral or memorial service is designed to bring peace to those left behind, and I would argue that the first time Jesse went to Terabithia without Leslie, he holds a sort of memorial service for her.

It soon transpires that May Belle has attempted to follow him into Terabithia and had gotten halfway across the makeshift tree bridge before becoming too scared to move forwards or backwards. Jesse rescues his sister, and the two make amends after Jesse had slapped his sister in the face in the previous chapter.