Canadian immigration law has its own definition of common-law partner. It’s someone who you’ve lived with, for at least one year, in a conjugal or marriage-like relationship. They don’t have to be the same sex as you.
It also includes a conjugal partner, if you could not live together because of laws that would punish you for it, or because you’d be persecuted.
For example, you might come from a country where your relationship is against the law.