What is heterosexuality?
Heterosexuality is a sexual orientation; it is one of the three main categories of sexual orientation (along with homosexuality and bisexuality). Until recent times, the majority of humans were heterosexual. Today, the situation is changing - according to a recent study, only 48% of individuals aged 13 to 20 self-identify as "exclusively heterosexual".
Straight pride flag
There are several versions of the heterosexual flag; there is no officially recognized straight pride flag yet.

One of these designs that were made to represent straight pride, a countermovement to gay pride, consists of five horizontal alternating black and white stripes. There is nothing wrong with this flag except for the fact that it is used mainly by homophobic people.
A variation of this flag, otherwise referred to as the straight ally flag, is more appealing - it represents straight individuals who are LGBT allies:

It was created in the late 2000s. This flag, just like the previous one, has five alternating black and white stripes; it also has a rainbow-colored letter "A" in the center that stands for the word "allies".
History of heterosexuality
However, heterosexuality is not the same as a heterosexual act resulting in reproduction - it is a concept, a historical phenomenon. In other words, heterosexuality is not the activity itself - it is a categorization of this activity.
Essentially, there was no necessity for a term that describes heterosexuality until scientists felt the need to contrast it with other phenomena, such as homosexuality and bisexuality, and that happened in the late 19th century. Different sexual behaviors, of course, were identified (and often forbidden, too) long before that. But the emphasis has been always put on the act and not the agent.
In 1901, just about a decade later, Dorland’s Medical Dictionary gave the following definition of the term heterosexuality: “abnormal or perverted appetite toward the opposite sex”. Here is the 1923 Merriam Webster’s New International Dictionary definition: “morbid sexual passion for one of the opposite sex”.
Apparently, society had a very different idea of what it means to be heterosexual back then compared to the modern understanding of this concept. Only in 1934, the same dictionary, to be more precise, its Second Edition Unabridged, explains heterosexuality as something we are familiar with today - “manifestation of sexual passion for a person of the opposite sex; normal sexuality”.
Almost all religions existing on the Earth believe that heterosexual sex is allowed within marriage. Speaking of which, most world’s religious traditions see marriage as acceptable exclusively between a heterosexual woman and a heterosexual man.
Until recently, heterosexuality was basically viewed as the natural inclination or even an obligation by both males and females. It was (and still is) assumed, promoted, and enforced by patriarchal society.
Debates about sexual orientations that still go on nowadays focus on the concept of heterosexuality being natural. Because heterosexual sex can result in the procreation of humankind, it is awarded a special “honorary” status. But nature does not obligate people to be heterosexual.
Historically, heterosexuality was necessary because humans (especially men) needed to demonstrate their power, show who they were, and defend their right to be where they were. Now that people are learning to study, understand, and show their weaknesses, fears, and desires, they do not seem to have the same need for being heterosexual as their ancestors.
To put it another way, heterosexuality has been losing its “high ground”. Perhaps because humans have been achieving more and more rights to express their sexual identities and more and more of them have been revealing their true sexual orientation.