Euro centrism revolves around the way in which European (or the entire Western world) think, behave, and act. Seeing everything through the lens of European views helps to justify their colonization. For example, during the Scramble for Africa many European countries started to colonize different parts of this continent. Their reasoning behind this was to "civilize" and "spread Christianity" to these societies.
This idea that they are "helping" these citizens by changing their political and economic structure shows that Europeans thought their beliefs, views, and ways of organizing a society where superior to others. This viewpoint results in Europeans forcing their culture and way of life on individuals who never really sought their ideas.