Writing patent claims is analogous to describing multidimensional jigsaw puzzle pieces using words. Your claims have to fit in the spaces between prior art.
Patent claims are the most important part of a patent because the claims are legally enforceable. Claims are also the trickiest part because they have to follow many rules. Claims should describe your invention, not read on the prior art, and not be obvious variations on prior art. Claims should also be precise enough that others can clearly determine what it is that you are claiming. Claims are also important for determining inventorship, and patent ownership.
Like a jigsaw puzzle: As a useful analogy, consider each patent claim to be somewhat like a multidimensional jigsaw puzzle piece. Each claim should be written using words and clauses that, in addition to describing your invention, “bend in” to avoid prior art, and “bend out” when there is no prior art.
From the patent examiner’s standpoint, he or she is looking at your claims in the context of the other prior art (the other pieces). The examiner is determining if each of your particular claim “pieces” is fitting nicely into the holes between prior art, or if they are hitting the other prior art “pieces”. If there is overlap, the examiner will, at a minimum, want you to make your claims “bend in more” to avoid that prior art. Part of the process of writing patent applications is to try to anticipate where this might happen and to write the patent in a way that gives you more options to “bend in” and “bend out” during the patent examination process.
There is one big difference between jigsaw puzzles and patent claims, however. In jigsaw puzzles, although the different pieces can’t overlap, the gap between the different pieces can be made very small. Think of this gap as the area where, given that one piece is “bending in“, it is “obvious” that the other piece must “bend out“.
Unlike jigsaw puzzles, examiners often require that this “gap” be big enough so that the shape of your jigsaw puzzle piece (claim) is not immediately obvious in view of the shape of the neighboring pieces. In fact, a big part of the patent examination process is negotiating the extent of this gap, and how best to amend the claims accordingly.