For context, their relationship started with Rainbow Dash and Twilight being girlfriends. Dash expressed that she has always felt that she has room in her heart for more than one mare, and Twilight realized she felt the same. The two dated around some, but never found anypony to really complete their herd. Sure, a few mares were welcomed into the relationship, but none stayed for long. Things went on like this for quite some time, until Fluttershy, reentered the dating scene. Flutters had been in an on-again-off-again relationship with Discord, and finally the two realized that what they had wouldn't last, and split on good terms before feelings got hurt. Rainbow, Fluttershy's life-long friend, was there for Flutters when the relationship ended, and while it was amicable, the yellow mare was a bit heartsick to be alone again. Things quickly moved past friendship, and Dash began to actively court a very willing Fluttershy. Twilight was more than willing to allow this, but never really felt the same heart melting puppy love for Fluttershy. Dashie and Flutters were happy, and so was Twilight. Only when Flutters moved in and Twilight got to know the more, ahem, private, parts of Fluttershy, did she begin to develop feelings. Before long, the three mares were content and all equally satisfied and well-loved, and a wedding followed soon after, and then came the small army of foals. Twilight is Mama, Dash is Mom, and Flutters is Mummy.

Twilight + Rainbow
These two are like an old married couple, and love each other deeply and sweetly. They enjoy long flights at night, reading together, and picking up hot young ladies on a Friday night. They are a jock/nerd power couple, and are excellent parents. Twilight and Dash are perfect for each other, and balance out the others faults.

Rainbow + Flutters
Their love is sickly sweet, all flowery poetry and picnic dates. Fluttershy is constantly showered with affection, always giggling sweetly when dashie presents her with a bunch of flowers with the roots still attached. As a pair, they aren't the best for discipline, but both love to show their foals new things and teach them through experience.

Twilight + Flutters
Their love is all passion and heat, and while they work as a couple, their relationship is rooted in physical attraction. When Dashie isn't around to play middle-mare, these two are like two rabbits, and the only biologically conceived child in the household is a product of their lovemaking. They work very well as parents though, they have the patience to have hard conversations with their foals, and teach them the complicated parts of life.

I want to make it very clear, that Twilight and Fluttershy do in fact love each other very much, and enjoy being married and raising a family together. but at the end of the day, their feelings for one another came to be after they started sleeping together. These things happen IRL and it is totally valid for a relationship to start this way.