Reduce blurring/smearing of the letter edges around small areas of the stencil:
The gaps are additional connections from the primary area of the stencil into an area with a small shape. The additional supports are placed such that any small shape is always provided with at least two connections, from different directions, back to the primary area of the stencil. This helps keep all areas of the stencil in a flat plain as much as possible which significantly improves the quality of the lettering deposited. In addition, this additional structural support while handling the stencil increases the useful life of the stencil.
While applying paint:
Having the stencil remain flatter to (closer to) the surface being stenciled significantly improves the look of the resulting lettering. The farther an area of the stencil is from the surface the more likely that paint will not have a sharp edge when applied. When the stencil is not close, paint will migrate under the stencil leaving blurring/smudges). These extra supports help pull these areas of the stencil into close contact with the surface being painted. Thus, having the extra supports improves the look of the lettering deposited when the stencil is used.
When removing the stencil:
This extra support is also important when removing the stencil from the area after the paint has been applied. Once the paint has been applied, the edges surrounding the painted areas will be tacky to the surface. How much adhesion there is will depend on the type of paint used and how the paint was applied. This can be anywhere from minimal to significant. Having the extra supports helps all areas of the stencil to be removed from the surface uniformly. If the supports were not there, the smaller areas would deform causing them to move slightly along the surface being painted and dragging some paint with them. This would result in the there being more blurring/smearing of the edges in these areas.
Improve the durability of the stencil:
Durability, as other posts have mentioned, is also a significant concern. The extra supports prevent the smaller areas from freely bending along a single support to the primary area of the stencil. Most stiff materials tend to become weaker the more a particular area is bent. This is particularly true for paper stencils when they become wet (e.g. from paint). In addition, any bend that is beyond a certain degree does not return to fully flat. Having the extra supports greatly reduces any bending in these areas and makes their connection to the overall stencil much stronger. This provides a significant increase in the usable life of the stencil.