These extra pieces are a help to stiffen the top and to keep it from warping.

A boxed top may have the top board flush with the sides, Fig.

285, E.The disadvantage of this is that the top may shrink and part from the sides and give a bad appearance.
The overlapping top, Fig.

285, F, obviates this trouble of shrinkage and adds a decorative element.

In this case the top may be glued on or screwed from below thru the side strips.
The top may be mitered into the sides, Fig.