Representation, under the perspective of political science, refers to the act of speaking up and acting upon the best interests of the constituents who voted for a specific leader. Constituents often vote for a representative based on their principles, ideals, action plans, and leverage in the community. However constituents also tend to vote for a representative (i.e., councilman, senator, major, governor, president, etc.) based on their superficial traits such as charisma, physical appearance, ethnicity, and even resemblance to some other person whom the voter connects to.
It is a sad reality but the latter type of voting does occur among voters who do not research their candidates and end up voting for a popular politician rather than for a good politician. This is when descriptive and substantive representation comes in.
Descriptive representation constitute a segment of politicians who represent the larger population from which they come. These are representatives that advocate in the name of a specific group or groups that are homogeneous to the background of the politician. Hispanics voting for Hispanics, etc.
Subjective representation would be the tendency to vote, through an informed process, by someone who represents the thoughts, ideals and principles that you as a citizen want to see safeguarded. For example, even though I am not gay and I am not HIV, I am very concerned as a citizen that the rights of these individuals are respected and I want to ensure that they are safe, regardless of our different backgrounds. Hence I would vote for a candidate with ideas similar to mine to ensure that this happens.