Primus inter pares is Latin
for "first among equals". This phrase is usually used when talking about a certain group of people (often from a specific profession) one of whom is above the others for some reason.
This phrase can be used for any peer group, often to show someone with outstanding abilities. So a pupil could be seen to be 'primus inter pares' since she/he is first among their peer group.
For example, the Prime Minister of the UK is considered 'primus inter pares'. He is a minister but is considered the most important of the ministers (his position started out as a simple minister who had to represent the views of the monarch at the time, there was no special post of Prime Minister). This idea has a political influence since the first among the equals is often seen as "one of us" rather than some detached, super being. This means that the Prime Minister may be the leader of the government but he is still just a minister and can be attacked in Parliament just like all the other ministers. He also has the same responsibilities of other ministers so he has to accept collective ministerial responsibility like the other ministers. He also has to listen to the rest of the government, if the backbenchers or his Cabinet colleagues do not want to do something, he can't just tell them to sod off and do it anyway.
This is in contrast to the President of the USA. The President is a seperate entity from the legislature (unlike the Prime Minister in the UK since the Parliamentary system has a fusion of the executive and the legislature). This means that he is not controlled by members of his government who are the same as him. In fact he is treated as better than many others in the government (this is only speaking from personal opinion from what I have learnt about the USA President). For example, the insistence of everyone standing when he enters the room, or the incessant need of calling him "Mr. President". This is unlike in the UK where the idea of primus inter pares stands and so the aforementioned practices would seem degrading of the other ministers.