Phenomenology is the careful description of lived experience: how things actually present themselves to consciousness, before theory and inherited assumption have reorganized them.
Edmund Husserl founded it, taking from Brentano the thesis that consciousness is always consciousness of something, and building a method around bracketing the natural attitude. Set aside the question of whether the world exists as we assume, and describe accurately how it is given. The aim was rigor, not skepticism. Husserl wanted philosophy to become a genuine science of the structures of experience.
His students took it somewhere he did not intend. Heidegger argued that the detached observing consciousness Husserl described is not primary at all: we encounter the world first as absorbed practical involvement, and the theoretical stance is a derivative mode that shows up when something breaks. Merleau-Ponty made the body central, arguing that perception is a bodily engagement with a world already meaningful, not a mental representation of one. Schutz turned the method to the social world and the taken-for-granted structures of everyday life.
Its political uses come mostly through that attention to the first-person situation. Arendt analyzed action, plurality and appearance from the standpoint of an agent inside the world instead of an observer above it. Beauvoir and Fanon used phenomenological description to show how oppression is lived and not merely suffered. Habermas took the lifeworld from the tradition and set it against the systems that colonize it.
The recurring objection is that careful description of experience cannot by itself settle what is true beyond experience, and that the tradition's characteristic vocabulary makes it unusually hard to tell when an insight has been established and when it has only been asserted.