We present high-resolution, high dynamic range narrow-band images of the extended narow-line region (ENLR), as well as broad-band continuum images, of the type 1.5 Seyfert galaxy NGC 4151. An "excitation map" is obtained by division of the calibrated [O III] λ5007 image by the Hα image. This line-ratio map shows that the brightest part of the ENLR, which is located between P.A. 210° and 240° with respect to the nucleus, comprises a string of high-excitation knots. A halo of lower excitation is found around the nucleus and to the northeast. The nuclear ionizing continuum inferred from UV and X-ray observations is found to be sufficient (to within the errors) to ionize the ENLR only if all available ionizing photons reaching the ENLR are absorbed by it and if there is no attenuation of UV photons by broad-line region clouds in the direction of the ENLR. The structure, excitation map, and energetics of the ENLR suggest that it is photoionized by a nuclear continuum which is collimated in the direction of the ENLR. The nature of the collimation of the ionizing photons is briefly discussed. Possible processes include: (1) beaming by a mildly relativistic jet, (2) shadowing by a dense obscuring torus whose axis coincides with the jet, (3) absorption by a nonspherical distribution of broad-line region clouds of large covering factor, and (4) the intrinsic "polar diagram" of a "naked" accretion disk around a supermassive black hole. We argue that process 1 is unlikely to be relevant. Process 2 is also improbable if the gas in the ENLR lies in the disk of NGC 4151, for the obscuring torus would then be viewed edge on and hide the broad-line region and the nuclear optical, UV, and soft X-ray continua from our view. We briefly discuss the possibility that the extended X-ray emission discovered by Elvis et al. may represent electron scattered nuclear emission.