Dictionary definitions of monogamy usually describe it as either the practice of being married to one person at one time (as opposed to polygamy or bigamy) or as the practice of only having sex with one person who you are in a committed relationship with.
But in practice, monogamy has come to mean much more than just marrying one person at a time, or not having sex with anyone else. The ideal of monogamy (which is also sometimes referred to as compulsory monogamy) is something that describes a relationship that can only take place between two people and where all of an individual's significant emotional, sexual, and social needs are met by the person they are partnered with.
Thus people who are in a monogamous relationship but who flirt or maintain significant outside relationships (even non-sexual ones) may be thought to be behaving in a way that is a threat to monogamy.
The pressure to be monogamous is pervasive in many cultures, despite the fact that it is well documented that both human and non-human animals can thrive in a variety of relationship models.