This could mean a few different things but either way it's a neon sign flashing a message at you to say "you need to change something"!
In my first marriage I always said "if either one of us starts to have feelings for someone else, it means there is something wrong here." Never in a million years did I think it would be me, but in the end, it was.
You can get into a rut in your relationship and sometimes you do not realize it. You start to run on auto-pilot mode; doing the same things, going about your day the same way and basically coexisting together rather than being in a relationship with each other. Relationships are a living entity and require constant nourishment, love and attention, and when that stops happening, the relationship slowly dies.
Then along comes someone else who either drop dead gorgeous, and / or may show some interest in you; they represent something new, different, an escape from life as it is, maybe even giving you the attention you've been missing whenever you realize you've been missing it or not. This might happen to you, or it might happen to your partner.
This is not unusual if you've grown apart. Over time we change but sometimes in different directions, which means you are no longer ideal for each other and this represents a time where you need to seriously evaluate your relationship.
By the time I realized what was happening it was already too late for me; I was already out of love and the more he tried to fix it, the more I felt smothered and suffocated which only cemented in the feelings of wanting to go. So when this happens, for some people their relationship is truly over and that new person, whether they enter into a new relationship with them or not, was just a catalyst to make massive changes.
For some people though, the feelings are nothing more than just wanting to have a physical experience with someone new, it has no bearing on how much they love their partner. After being together for a long period of time, the newness and initial passion with someone you do not know is just like a new adventure; it's thrilling and exciting. Depending on how this is deal with though, depends what effect it has on the relationship.
Some people go ahead and have fun alone; cheating or having an affair, which has a high probability of destroying the relationship eventually. Often people will take this option if they're afraid how their partner would react if they suggested the idea having sex with the other person. Sometimes they just do not think about it and do it because they can … if that's the case then their partner describes someone better that will value the relationship and them.
Some couples talk about it openly and either use it as a fantasy to spark up their sex life, and some actually move into a swing style relationship where they get to explore new sexual experiences and get to have that "new" partner. I'm meeting more and more couples that are taking this road; they do not want to lose their relationship but they do want to have the experience of adding someone new to the mix, mostly together but for some people where one partner is traveling, it's a way of having some fun when they can not be physically together. (To find out more about this kind of relationship before making the jump – read The Ultimate Swingers Guide).
There are a plethora of options and reasons why having feelings for someone else is happening for one or both of you, but the underlying message for you is to take a good look at your current relationship and make changes that are going to move you both in a direction that makes you happy, whatever that direction may be.