When a person is cisgendered, they identify as the gender that matches the sex that they were assigned at birth. Cisgendered is, as such, a complementary designation to the term transgendered.
A transgendered woman is a person who was assigned male at birth but who identifies as a female, while a cisgendered woman is a person who was assigned female at birth and identifies as female.
It is important to understand that, although the terms are frequently used interchangeably, sex and gender are not the same things. Sex, in scientific terms, is a biological and physiological designation. It refers to both a person's chromosomes and the way that their genes are expressed (XY individuals can develop physiologically female bodies if they have certain genetic conditions that affect hormone processing.) In contrast, gender is a social construct. It refers to the social roles, behaviors, and expectations that are thought to be appropriate for men and women. Masculine and feminine are adjectives describing gender characteristics. Male and female describe sexual characteristics, although they are sometimes also used to describe gender.
Gender identity and sexual orientation are also not the same thing. A cisgendered person can be either heterosexual or homosexual, and so can a transgendered person. This is, in fact, one of the problems with lumping transgendered individuals into the GLBT (or GLBTQ or GLBTQQI) acronym. It makes it more likely that people will conflate gender identity and sexual orientation when they are two entirely different spectra.
Most STD research has been done on cisgender individuals. There is not nearly as much data about STDs in transgender men and women. In part, this is because the physical risks experienced by transgender individuals are so diverse. Some choose to undergo hormonal treatments and/or surgery to make their bodies more closely match their genders, while others do not. This makes it difficult to make broad generalizations about biological risk, although behavioral risks are similar for all sexually active adults.
It is worth noting that, just as the word for working on the assumption that all people are heterosexual is heteronormativity, the word for working on the assumption that all people are cisgender is cisnormativity. This is different than gender essentialism -- the idea that males and females must behave in certain, gender-specific ways.
Many sexuality educators, LGBT activists, and individuals who are cognizant of gender politics use the term cisgender to reduce the stigma associated with a transgender identity. It is easy for people say things like "transgender as opposed to normal gender" when describing individuals who identify as a gender other than the one they were assigned at birth; however, that implies that transgendered people are not normal. Using the term cisgendered, in contrast, does not assign a relative value to either gender identity. Instead, it accepts transgendered and cisgendered identities as equally valid ways to experience gender.