The term cisgender sounds like it comes with a long and tarried history and movement, like transsexuality, that finally has a word to encompass a new class of gender.
And while the term certainly did come up as part of a burgeoning sexual revolution and social movements that accompanied these, cisgender is more of a recognition to contrast against its "opposite": transgender. In other words, the two terms are intricately tied.
Gender is a whole host of biological, behavioral and psychological performances, impulses and tendencies. Those who don't experience their gender as aligned with how they identify, usually end up coming out as transgender later on in life. Keep in mind, however, that this discomfort and this recognition may begin early on in life and develop as the individual does.
Cisgender, then, is the experience of gender where an individual feels that their outer gender and inner identity are in complete alignment. This means that "cis men" are men who have been assigned as "male" at birth, and continue to identify as male, with no apparent discord caused by "feeling" female.
For women, it's the same: cis women experience their assigned sex of "female" as being in alignment. In other words, they feel female.
The term cisgender, then, is more of a consequence of transsexuality, at least insofar as the coinage of the word itself. There was a need to contrast and assign an identity to those who don't identify as transgender.
Note also that the term has everything to do with gender and that sense of the inner and outer identity being "aligned" -- but does not necessarily denote sexual preference. This means that a cis man or woman may still prefer gay and lesbian partners and relationships or display other sexual preferences such as pansexuality.
Men and women who are "cis"-gender or who recognize and claim this status are usually cognizant of and sensitive towards those who are transgender. It's a handy way to define oneself as a "friend of" or "advocate for" the movement of gender choice without imposing one's own ideas and preferences.
Cis males and females, when using this term, can indirectly say that they're proponents of the idea of gender fluidity as well as sexual preference non-fixity. In fact, identity itself is half experiential, half physical, so it's hard to say where one ends and the other begins.
The term cisgender also liberates those who don't necessarily abide by "heteronormative" sexual standards but, at the same time, also don't experience their genders as other than what they were assigned at birth. Recognizing one's gender is an important part of exploring one's sexual identity.
It may be said that, at the end of the day, these are all words and terms -- in other words, aren't we just playing semantics? But language matters -- because we use our laws to assign rights to classes, denoting some as protected and minority. Without the normalization and mainstreaming of these words, how can we recognize all classes as equal?