Assigned Sex refers to the social concept aka sex you were assigned at birth and most likely raised as. It essentially refers to the sex that was put on your birth certificate, without making assumptions about your actual/current sex or body. The concepts of "genetic", "biological", or "birth" sex can be problematic for transgender people as it makes it sound as if they aren't "real" men/women/non-binary, or are less so than a person who's cisgender. Also, phrases like "bio-guy" or "genetic girl" confuse gender and sex, as guy/girl usually refers to gender identity- not genitalia. This further others trans people and makes their gender seem less valid.
It also can make describing things regarding intersexed people  a bit easier. Many intersexed people were assigned a sex that does not match their chromosomes, genitals, and/or anything else about their body, or were subject to non-consensual normalization treatments  which altered their body without their knowledge or permission.