What does it mean when a patent is cited as prior art in another patent?

No. When a prior patent is cited as prior art, it usually means that the patent disclosure substantially shows what you are claiming in your patent application. Your job is to then amend your claims, if necessary, to insert something into your claims that is not disclosed, or an obvious difference from what is disclosed, within the patent. Sometimes the examiner, of course, may be wrong - he may say that the patent discloses what you are reciting in your claims, but that is not always the case - in that case, you can argue for patentability of your claims without amending them.

The patent owner would only be due royalty or other arrangement if your invention infringes one or more of his claims - to infringe a claim, your apparatus, for example, must include every element recited in one or more of the patent claims. If your invention does not comprise each and every element recited within one or more of the patent claims, you do not infringe and do not owe any royalties.

To expand a little on Steven's answer, you only infringe a patent by what you do commercially, not by what you say or show in a patent. So your invention only infringes at all if you are offering your invention for sale etc...

Still, if you are infringing, then showing your design in your own patent application might alert the patent owner. In fact we did recently find an infringement because we noticed someting the same as our invention in another company's (later) patent drawings. Our patent was cited as prior art against theirs. Their patent application was just the clue that infringment might be happening, however. It was not infringemetn in itself. We then had to find the actual product on sale and compare the product features with our patent claims.