'Processing' refers to the generation of a visible image on the film.
The film, as you receive it from Kodak, is a transparent, flexible, acetate base (made from cotton) with a coating of silver halide crystals suspended in gelatine. As you run the film through your camera, photons of light become trapped by the silver halide crystals, recording patterns of light as the invisible 'latent image'. Immersing the film in the developer causes a chain reaction, and crystals holding a photon react to form colour dyes, making the image visible.
If you think about it, you will realise that the places where the most light lands will form the most dye, and thus become the darkest areas on the film. So the most light parts of the world, become the most dark parts of the film. This is what is meant by a 'negative'. After processing, negative film used to be printed to make a positive, however nowadays film is scanned to digital and inverted. So processing is done first, and then scanning (also called 'digital transfer' or 'telecine') and the digital version is inverted - to get back to light things looking light, and dark things looking dark.
See Memorylabfilm.com for all processing enquiries.
If you are filming images for immediate consumption and will have no further interest in the film later on, you can choose not to receive your films back in the mail. Film will NOT be kept - films left at the lab will be used for testing and other purposes that will result in their destruction. If you lose your data you will not be able to scan it again unless you have the film posted to you.
If you are recording precious memories or doing creative work you really should opt to have the film posted back to you. Film will last 50 to 100 years, whereas your digital copy will last 1 -5 years typically. Keep the film and it will be able to be scanned to future digital formats.
The process used for Kodak's Vision3 family of films - 50d, 200t, 250d, 500t. This is the process described above, where light parts of the world become dark parts of the film. What was not mentioned above is that colours are opposite to reality as well - green things are magenta (purple) on the negative, blue things are yellow, red things are cyan and so on. There is also an overall orangeish cast to the image, which is a technical requirement to balance imperfections in the dyes and give truer colour when printing onto colour print film. Another feature of ECN processing is that it is a very low contrast process, which gives maximum exposure latitude to the recorded image. This is great for printing, and means that scans will have a lot of wiggle room for making decisions about colour, contrast and brightness. The downside is that you do have to do a lot of powerful 'grading' to get from the completely wrong colours and very dull flat negative to a bright and colourful digital file. Fortunately, DaVinci Resolve is easily able to accomplish this colour correction, and is widely available.
This is the process for Kodak Ektachrome 100d (the last of a very long line of colour reversal films from many manufacturers). The reversal process yields positive images on the very film that you used in the camera, without requiring printing or a scan. In the past, all Super 8 film and processing was reversal, and to watch it required a Super 8 film projector. You would generally only have the one 'copy' of the film (which isn't really a copy at all, as it is the original film - called 'the camera original') which means there is no chance to correct exposure or colour balance of the images. Projected camera original film is a thing of extraordinary beauty, but only if your exposures in the camera were quite perfect. Very few labs offer colour reversal processing. The last colour reversal process to be widely offered was called E6 - it may still be available in the US at Dwayne's Photo, Pro-8mm or Spectra. If you have found an old (>20 years) roll of super 8 it is almost certainly Kodachrome - we recommend sending it to Film Rescue in Canada, who can process it as a black and white negative and scan it to digital for you.
Nowdays you are more likely to find a lab that will process colour reversal stocks (i.e. Ektachrome) in colour negative chemistry. This is a 'cross process'. The result is a colour negative that yields slightly inaccurate, but usually satisfying colours, suitable for scanning to digital. It is not suitable for traditional film projection. It can be a desirable 'look' - however, results vary greatly depending on exposure accuracy.
Super 8 films Kodak TriX, Kodak Plus-X, ADOX panX, ORWO UN54, Kahl 21, and 16mm films Kodak Double-X, Kodak Tri-X, Fomapan 100R, Fomapan 100, Fomapan 400, Foma Cine Ortho 400, Orwo UN54 and Orwo N74. Black and White films can be processed as negative or as reversal, though some stocks are optimised for a specific process. Fomapan 100R has a silver anti-halation layer that cannot be removed without a reversal bleach stage - it must be reversal processed or will be very thick and muddy. Kodak Double-X is very grainy and contrasty if processed reversal and is much better as a negative. Orwo UN54 is specifically designated as 'Umkehr/Negative' meaning reversal/negative - it is happy either way.
For the sake of completeness I should mention this one, the complementary process to ECN. ECP is used for developing prints struck from negatives onto Kodak 3383 Colour Print Film. It is a beautiful thing, with very high contrast and super-saturated colour - but only the really big labs still do this (in the US that is Fotokem in LA and Colourlab in Maryland, in Europe a few high priced bespoke outlets) - and the very smallest labs- that is the Artist-Run Film labs. If you are the D-I-Y type 3383 is cheap and very difficult to work with, but gives pretty amazing results for experimental work, when you get to know it.