Every society on Earth has some degree of inequality and discrimination, in part because there is some human nature involved in how we treat and perceive others.
But if you are looking for examples of these inequalities, consider the following ways we find them in the world:
1) Race - America has elected its first African-American President, a clear example of social progress. At the same time, a majority of Caucasian voters did not support Obama. While certainly not all of that opposition or even most of it could be based on race, certainly a degree of it was, and racism in certain regions of the country, along with certain age groups (over 65) it tends to be more common.
2) Gender - Women on average still earn only 77 cents for every dollar earned by a male. A small minority of elected officials are female, even though they represent almost 53% of the overall population. Women are equal in law, but not yet in social practice.
3) Education - Everyone has the right to attend school in the United States, but that doesn't mean the schools, the teachers or the education is equal. Inner city schools are notoriously underfunded and staffed. Schools with more violence and crime could be said to be discriminating against those who are poor based on where they are forced to live and attend school.
4) Class - Those who live in poverty are forced to live in places they can afford, while the wealthy are able to live wherever they want. They are also able to afford more fire and police services, better schools and health care, while those in poverty have all the rights of ordinary Americans, they face economic discrimination in their daily lives.
Social inequality with regard to gender exists when one sex (usually female) is discriminated against in formal and/or informal ways in a society. This discrimination often leads to situations in which women have less power, fewer rights, and/or less of an ability to make money than men do in that society.
Gender inequality can be severe and obvious or it can be more subtle. For example, it can be manifested as in Saudi Arabia where women are required to have male guardians who make important decisions for them. By contrast, it can also exist in places like the US in more subtle ways. In the US, it can manifest itself in terms of women being underrepresented in positions of power.
The reasons for and the impact of gender inequality is a major field of study in social sciences.