Seconds is short for secondary image choice or secondary image selections. In culling through images the photographer selects images that represent the best for a given shoot. During this process some images are deleted (because they're unusable due to blur, misfires, camera setting errors, etc.) and the remaining are the seconds.
Let's suppose, for the sake of this example, that the photographer selects 10 of the 50 images to process. Of the 40 remaining, 10 of them are tests, errors or so blurry that they get deleted. That leaves 30 images as seconds from this photo shoot and they get segregated and saved. It doesn't stop here;
The photographer then turns over his primaries (the initial 10 he edited) to the client. Of those ten images the client will select only one for print. The remaining nine then become the client's secondaries. So now you know what secondaries are. Yeah, I know... long explanation.
There are various schools of thought regarding what to do with secondaries, specially when storage space is of an issue. One thought is to clear the way and just get rid of them. After all, you've already picked out the best of the best. No need bothering with files taking up space. The other school of thought is just the opposite. You never know if you'll ever have a need for them. After all, additional digital storage space can be bought as the need arrises.
Those two views are obviously oversimplified but it illustrates two viewpoints. I am of the second opinion, keeping seconds for those just in case moments. Let me explain why.
As an editing resource: This is my primary concern, specially with outdoor shoots or shoots where you have little control of the environment. Having seconds allows me a certain flexibility in editing as I can take information from one of my seconds to correct a problem in the primary. For example, I did a shoot of a couple next to their car at a local park. In the background was a trash receptacle, the big ugly kind. Right next to that was a bright orange safety cone. Behind those was a bush. The angle was such that any cloning of the bush would have resulted in too much of a repeating pattern. Fortunately I was able to take that same bush form one of my seconds, shot from a different angle, and use it to remove those ugly items.
Other examples can include something as simple as multiple people where one person was caught mid blink. Having a good second will allow you to clone a better expression into the shot. Unwanted background elements are easier to eliminate if you have a second image without those elements in them. That's useful for landscape photographers. For photographers who shoot for publication, having slight variations allows you to modify the shot to meet very specific requirements. A slight shift of a face (or even just the eyes) can make or break an image. Having multiple options allows an art director to make the appropriate selection.
As an alternative view: This is where you need to show a slightly different view of the same subject. Being able to pull from additional images makes that part of the job easier. Often these alternatives come up last minute or even months down the line and usually as an unplanned addition. Experienced fashion and product shooters tend to allow for this from experience so having these extras available is good planning and saves the cost of a reshoot.
A good art director will have all the bases covered but sometimes even the art director is broadsided by a client. You'll be a hero if you can produce the requested additions. Alternative shots are also useful for inclusion in a personal portfolio without using the client's image. Sometimes this can circumvent certain legal aspects of a release. Just make sure you fully understand the limitations of the release.
Republishing without licensing infringements: This also plays into contract law with first publication rights, etc. First publication rights allows you to set a higher rate for an image that is sold to one specific outlet for first time use. Once that first time use is sold you can't sell that right for that image ever again. However, if you have multiple, but slightly different, shots of an image then you can sell first rights on each of those. Just keep in mind that this is a risky move and can be construed as a dirty trick by some publishers. It's not so bad on a secondary market but you still need to be careful.
This also works if you want to keep within legal rights but still want to use an image, for example, in a blog. Using one of your seconds does not detract from the value of the primary image. Specially if the second looks less like the primary.
Behind the scene shot or miscellaneous images: Seconds can come from anywhere. Test shots, goofing around, experimentation, documentation, etc. I often find images for my blog or tutorials from the many seconds I have stored up. That awful shot taken on one of your outings may be just exactly what you need to illustrate a topic. I often find myself purposely taking random shots in anticipation of a potential tutorial.
Before deleting all those seconds off your hard drive, consider the potential of future use. Having that resource allows you to easily pull already captured resources without having to purposely shoot them. Having various resources for editing gives you a ready library of images to use for correcting problems in post production. Ultimately is about having choices.
Legal clarification: Another remote possibility is to contest legal ownership of an image. Occasionally the issue of image ownership comes up when two very similar images (or even the same image) comes under scrutiny. The photographer that can prove without reasonable doubt they authored that image will walk away the winner. Having seconds helps prove, through frame timelines, that you were indeed the author.
If you have a different use for your seconds, feel free to share them with others.