1) The market has become too fast paced.
There used to be a time where a game that became a smash hit, lasted at least a year in the top along with a runner up that always followed close behind, but that thing doesn't happen that often anymore as gaming companies are always trying to keep on each other toes almost making it a race for the gaming community. Competition can get fierce and sometimes that becomes a flurry of games coming in a very tight time span. Take for example the next coming months from September to the holidays, there will be a lot of game releases on different platforms. This is not only a wallet slayer, but also a very time consuming thing as most of these games have online modes that require a lot of play time in order to fully enjoy them. When this happens, some of the games fall through the cracks and are not picked by all the potential buyers they should, (especially when it is a type of gamer that is always keeping up with novelty) so a remastered version of a game becomes a second chance to catch those that didn't bought the game when it was released for the first time and a chance for some gamers to get a little extra for their money as a reward for still having interest in the game even thought is is not new anymore.
2) Busier gamers get a break.
Gaming is for life, but let's face it. A lot of gamers right now are part of the working class, have a family and/or personal projects to attend to, so they don't have the same amount of time as they used to before getting these responsabilities. Sometimes when a wave of games come by, they can at most play 1 or 2 titles at a time so in this case a lot of new releases are just left hanging. Some of you may be thinking "So what? They just have to buy the games they missed at a later time", but it isn't that easy when we consider that new games keep coming all the time and these people gaming interests often get divided and conflicted (online oriented games vs single player experiences) when time is scarce. This is the reason why remastered games nowadays seem to be a very appealing option for gamers who have that kind of time limitation, especially when the remastered version includes past DLC and/or gameplay extras.
3) It breathes some life into a generation that had a slow start.
This time around, compared to previous console generations, we are seen a much slower pace in early game releases as too many third party companies are still clinging to the previous generation. This had kept the new consoles on some sort of gaming drought that has been hitting for almost a year, with most of the anticipated heavy hitters still on the 2015 list. On this case, remastered versions (done right) serve to inject some interest when they manage to give a clear contrast between the previous and current generations. That contrast is one of the things the begins knocking on people's heads like a drop of water on a rock, until it breaks it and get them to support the platform because they actually see a tangible difference. An example of the complete opposite is the Wii U launch fiasco, where people thought that the new machine was just another Wii and did not ran to the stores to get it as they did with the Wii itself.
4) Keeps interest in the franchise.
We know that sequels on some famous franchises are almost a given, but these things take time. In order to keep the interest in the franchise going strong until that new game arrives, companies often use remastered versions and that is alright if they do it without the product been a cheap rehash of the same game and if the new version doesn't come a very long time after the original, like Zone of the Enders HD which was one that came too late to have any effect on a good franchise that was just lost in time due to several years of neglect. At this time, remastered versions of games that have been released in the last 2-3 years are good for their corresponding franchises as long as they make it count and don't try to low ball the gaming community or pretend that rehash from a 5+ year old game will sell the same as it did when it first came out. It is also worth pointing out that the success or failure of a game rehash SHOULD NOT be used as a barometer to measure the franchises worth (Konami, I'm looking at you).
5) Serves as exercise for game developers.
Right now, as many companies are still working with previous generation projects, it is a good thing for them to flex their developing muscle a little and warm up in the developing process of the new consoles. While they work with the new SDK (system development kit) tools that each console has to offer, they can get new ideas and test the implementation of various new things while working on a remastered version of their game. This makes it easier for them to explore their own concepts a bit and discover what new things can be implemented in the next game on the franchise. Of course, most of us don't see this happening as we don't have insider access to big game development studios, but in any developing environment (gaming and not) it is very common to make new ideas out of revisiting the old ones, spawning a lot of nice surprises and "aha" moments.
Wrapping it up
Based on how the videogame market is moving right now, remastered versions of games are not the dreaded money grubber scheme that they used to be. This is because we as a community have become smarter and by materializing our opinions with our wallets, we have forced companies into putting a little more effort into their game rehashes. It may be a temporary thing, but for now they seem to work and deserve a chance. Remember that if you support the franchise now, you are giving a clear message to publishers, saying that you will also support the new games that are to come in the future.