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For example, for Ilford Delta 100 I see listed development times for 50, 100 and 200, such as in this chart.
Are they referring to over and under developing times for the film? i.e. to develop normally (100), develop for 6 minutes. To under develop by a stop (50), develop for 4.5 minutes.
That's exactly what it means.
Delta 100 is an ISO 100 film, so if shot correctly and developed with Ilfosol S, the correct development time is six minutes.
If you'd overexposed the film by metering for ISO 50, you can't leave it in the developer as long, and they recommend 4.5 minutes with the same developer. This is called pull processing. (This is not something Ilford or most manufacturers recommend but is handy if you didn't set the camera properly.)
You can also push process film that was underexposed, which you'd do if you metered for ISO 200. Ilford doesn't have a recommendation for Ilfosol S, but if they did, it would be a longer time to allow more of the emulsion to react with the developer. If you look up at the Ilfotec DD-X row, you'll see that they recommend 14 minutes vs. 12 for normal development.
The blank boxes in the chart are combinations that either weren't tried or aren't recommended. (Probably the former.)
A lot of things happen when you immerse your film in a developer. Since the developer is primarily water, it wets the film. The emulsion consists of light sensitive salts of silver. These are imbedded in a binder (glue) made of gelatin. The water causes the gelation to swell. This action opens up the gelation structure which resembles a jumble of transparent spaghetti. The silver salts are imbedded between the strands.
Now that the structure is swollen, the developer is free to percolate within. The developer seeks only exposed salts of silver, and when these are met, it reduces them to metallic silver by liberating the halogen component (bromine – iodine – chlorine). The liberated halogens are dissolved into the water of the developer.
All this swelling, infusion and reaction take time. Fast films (higher ISO) contain more silver salts -- thus the process takes longer. Slow films with lowered ISO, develop more rapidly. Developer manufacturers test their solutions on various film emulsions and publish their findings in the form of a Time-Temperature table. The developing time is different for high speed films, because they contain much more of the light sensitive goodies.
We can push-process: This is adding developing time to force the film to perform with an ISO that is greater than intended. We can pull-process: This is reducing developing time to correct for an unintentionally over-exposed film.
Additionally we extend developing time to achieve results that upraise the natural contrast of the film (yield a harsher image). Conversely we reduce developing time to reduce contrast (flat image).
