What does standpoint theory mean in terms of the theoretical work and everyday lived realities of women and minorities? How did this standpoint theory build on the work of Karl Marx, especially regarding his view of the bourgeoisie and the proletariat?

Standpoint theory argues that how we experience and talk about the world is rooted in the totality of our own experiences. This moves away from the simplistic notion that all Latina women, for example, must think alike, because as well as being Latina, a woman might also be upper or lower class, a recent illegal immigrant or someone whose family has lived in the United States for many generations, a resident of a big city or a rural area, trans- or cis-gendered, young or old, etc. Standpoints are always intersectional. When we talk about everyday lives, they don't exist in a vacuum and cannot be understood through some singular perspective. Instead, the objective conditions of our lives are refracted through multiple simultaneous subjectivities.
The historical grounding of standpoint theory is Hegel's understanding of the nature of the master-slave relationship, something that Marx expanded into an analysis of class. The dominant group in a relationship does not just have objective power, but also ideological power; dominant groups control the way discourses about issues are framed. The problem with this is that the subjective viewpoint of a dominant group is not objective, but dominance allows some groups to control discourse and ensuing ideology, leading to what Marxists refer to as the problem of "false ideology." Standpoint theory attempts to correct this bias by examining how our fundamental assumptions about our world are determined by our position within the world.