What does it mean to be on the right wing and left wing?

They represent the two main political ideologies that we have develeoped.
The Right Wing take the stance that it is better for the people if they have as little government interference in their lives as possible. They also tend to be hands-off when it comes to businesses as well. The Right are also more isolationist, and encourage trade within your country, so all money remains withing your economy. As an extension of this, the Right tend to be more opposed to immigration. They also believe that minimal government interference and low taxation means that people should be ore responsible for themselves and securing their own economic security. As a whole, they are a conservative bunch, and value the old ways of life and are mistrustful of change. They are more generally associated with the establishment (e.g-monarchy or religion).
The Left, on the other hand believe that businesses manipulate and exploit their workers and are more pro workers' rights and unions. Because of this, the Left have a history of imposing stricter regulations on businesses. The Left are more supportive of welfare and providing a social security safety net for people so that if they are unemployed, the government will always look after them. However, the con to this is that they are in favour of higher taxation. They tend to be more socially liberal and receptive to new ideas (in other words, they are the ones who historically have pushed for womens' rights and more recently homosexual rights). And additionally, value links with other countries and trade with them more willingly, and believe that immigrants on the whole, enhance a country. They are more generally associated with progressiveness and reform.

I believe the terms come from the time of the French Revolution and in their chamber, those who were pro the monarchy and nationalism sat on the right and those pro the people and revolution sat on the left.

Extremes of both views are not good. Communism, such as in Soviet Russia and China is an example of the Left Wing ideology taken to its extreme, resulting in the deaths of literally millions, and Hitler and Mussolini were extreme Right-Wing thinkers.

Nowadays, the Conservative Party of the UK and the Republicans of America are moderate-right and the Labour Party of the UK and the Democrats in the USA are moderate-left.