This phrase comes up while Holden is describing to Stradlater how he used to play checkers with Jane over the summer. The entire passage reads as follows:

She wouldn't move any of her kings. What she'd do, when she'd get a king, she wouldn't move it. She'd just leave it in the back row. She'd get them all lined up in the back row. Then she'd never use them. She just liked the way they looked when they were all in the back row.

Holden idealizes Jane. He is horrified that someone as sneaky as Stradlater is going out on a date with her, so he begins babbling about her. Jane's keeping all her kings in the back row while she plays checkers is a metaphor for how Jane is quiet and reticent about her power as she plays the game of life. Kings are powerful pieces in checkers, and Holden is saying that Jane has power—that she is a strong person—but that she prefers not to show it. The metaphor also suggests that she is an artistic person first and foremost, because part of her rationale for not moving her kings is that she "liked the way they looked."

Of course, we have no way of knowing how much of this is what Jane really thinks and how much is Holden's projection.