It appears that the wood of my fence is shrinking and now you can see through the cracks into my back yard. What can I do to stop this? Is power washing the fence and staining the fence going to help reduce this?

It is natural for wood to shrink as it loses moisture. Did the person that sold you the fence tell you that it could not be seen through?

Wodd is in constant movement it will expand and contract until it rots. The only way to make a wood fence that can’t be seen through at all is to have the boards overlap so no gap opens. The wood has dried since the fence was installed. If the wood had been dried to a very low moisture level before installation and then installed tight the boards would have expanded and might be loose not rather than having gaps. Expanding wood can even break steel fasteners under the right(wrong) circumstances. The only fence I know of thet will not expand or contract and open gaps are those made from wood plastic composites or PVC. The gaps should not be wide enough for anyone more than a foot away from the fence to see through. Any finish that is applied will slow the wood movement but not stop it. The only way to stop wood movement is to impregnate it with plastic.