Monogamy is when you have one relationship at a time. It is the expected norm in vanilla relationships but is also very popular in the kink community too. In vanilla society, monogamists partner up with just one other person and that is often for many years at a time. Some get married, others have civil unions but any relationship between two people with a sexual/romantic connection is counted as monogamy.
Within BDSM the definition is slightly different, in that a monogamous Dom and sub are likely to keep most kink and sexual play between themselves. Strict monogamists will commit to only having kink or sexual play with one person.
The line between monogamy and non-monogamy is definitely blurred. However, there are those within monogamy who aren’t quite as strict. They may have exceptions to the rule of only being with their partner. For example, when it comes to play. If one partner is into a particular fetish or aspect of BDSM that the other doesn’t enjoy they may do this one thing with another, pre-agreed person from time to time. They may have agreements that allow for one partner to demonstrate certain BDSM play with others or that the person can be a rope bunny for another person under certain circumstances.