This paper presents high-resolution, high dynamic range narrow-band images of the extended narrow-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 forbidden 5007-A line image by the H-alpha image. This line-ratio map shows that the brightest part of the ENLR, which is located between P.A. 210 deg and 240 deg 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 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 discussed.