Not quite - the nanometres on the y-axis are "deltas" of your spectral variable. The density allows you to answer questions like "how much power am I getting per square metre in a range [A, B] of wavelengths". You would integrate your density between A and B to obtain the value.
For example, pick some small value "k" close to 0 in units of nm. Then in your example, the amount of irradiation contributed by the small window [1000-k, 1000+k] nm of wavelengths is roughly equal to k*3.5e18 photons per square metre per second (you can check that the units work out). The smaller k is, the more accurate the approximation. If you want to get an answer for a larger interval you can break it up into lots of k-sized pieces and sum the results up. Recall from calculus that this is exactly what integration is (yes, I know the truth is a little more complicated in general measure theory).
Does that help? It's a bit like a continuous probability distribution, in the sense that to get an actual probability out of it you have to integrate. Formally a mathematician would say that a density corresponds to a "measure" over the space of all possible values of your spectral values.
For example, pick some small value "k" close to 0 in units of nm. Then in your example, the amount of irradiation contributed by the small window [1000-k, 1000+k] nm of wavelengths is roughly equal to k*3.5e18 photons per square metre per second (you can check that the units work out). The smaller k is, the more accurate the approximation. If you want to get an answer for a larger interval you can break it up into lots of k-sized pieces and sum the results up. Recall from calculus that this is exactly what integration is (yes, I know the truth is a little more complicated in general measure theory).
Does that help? It's a bit like a continuous probability distribution, in the sense that to get an actual probability out of it you have to integrate. Formally a mathematician would say that a density corresponds to a "measure" over the space of all possible values of your spectral values.