Optical and ultraviolet observations of the Type IIn supernova 1995N at epochs between 321 and 1799 days after the explosion show three distinct velocity components. The narrow lines come from circumstellar gas and show both low and high ionization. This component has a low filling factor, and is photoionized by X-rays from the shock. The intermediate component, which is dominated by newly processed oxygen, originates in a shell with velocity of 2500-5000 km/s, and most likely comes from the ejecta. The hydrogen- and helium-dominated gas has a low ionization, a high density, and velocities that extend out to ~10,000 km/s. Strong signatures of Ly-alpha-pumped fluorescence lines of Fe II are seen in the near-infrared and ultraviolet. The He/H ratio, ~ 0.3 by number, and the nitrogen overabundance provide strong evidence for CNO burning products. The fluxes of the broad hydrogen and helium lines decrease considerably faster than the oxygen lines. The H-alpha line profile shows strong evolution, with the red wing decreasing faster than the blue. Possible scenarios, involving either a clumpy circumstellar medium, or an aspherical distribution of the surrounding gas, are discussed based on the line profiles and physical conditions. Finally, we propose that Type IIn supernovae have their origin in red supergiants in a superwind phase. ; Comment: 49 pages, 14 figures. Submitted to ApJ