The cosmic infrared background (CIB) includes roughly half of the energy radiated by all galaxies at all wavelengths across cosmic time, as observed at the present epoch. The PACS Evolutionary Probe (PEP) survey is exploited here to study the CIB and its redshift differential, at 70, 100 and 160 μm, where the background peaks. Combining PACS observations of the GOODS-S, GOODS-N, Lockman Hole and COSMOS areas, we define number counts spanning over more than two orders of magnitude in flux: from ~1 mJy to few hundreds mJy. Stacking of 24 μm sources and P(D) statistics extend the analysis down to ~0.2 mJy. Taking advantage of the wealth of ancillary data in PEP fields, differential number counts d 2N/dS/dz and CIB are studied up to z = 5. Based on these counts, we discuss the effects of confusion on PACS blank field observations and provide confusion limits for the three bands considered. While most of the available backward evolution models predict the total PACS number counts with reasonable success, the consistency to redshift distributions and CIB derivatives can still be significantly improved. The new high-quality PEP data highlight the need to include redshift-dependent constraints in future modeling. The total CIB surface brightness emitted above PEP 3σ flux limits is νIν = 4.52 ± 1.18, 8.35 ± 0.95 and 9.49 ± 0.59 [nW m-2 sr-1] at 70, 100, and 160 μm, respectively. These values correspond to 58 ± 7% and 74 ± 5% of the COBE/DIRBE CIB direct measurements at 100 and 160 μm. Employing the P(D) analysis, these fractions increase to ~65% and ~89%. More than half of the resolved CIB was emitted at redshift z ≤ 1. The 50%-light redshifts lie at z = 0.58, 0.67 and 0.73 at the three PACS wavelengths. The distribution moves towards earlier epochs at longer wavelengths: while the 70 μm CIB is mainly produced by z ≤ 1.0 objects, the contribution of z > 1.0 sources reaches 50% at 160 μm. Most of the CIB resolved in the three PACS bands was emitted by galaxies with infrared luminosities in the range 1011 - 1012 L&sun;. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.Appendix and Tables 4, 5, 8 and 9 are available in electronic form at http://www.aanda.org