Prof. R' Mordechai Z. Cohen at Yeshiva University is renowned for his explanations of the different styles of the Parshanim. His explanation of Rashi, to which I cannot do justice, can be basically understood in the following phrase often used by R' Meir Goldwicht (not a phrase R' Cohen uses): 'Omek HaPeshat.  

As R' Goldwicht uses the phrase, it means, in a nutshell, taking all of the surrounding context into account before analyzing and approaching the Peshat of the text (in his case, Gemara). R' Goldwicht would highlight what a lot of Yeshivoth call "Gemara Be'Iyun" - Gemara, Rashi, Tosafoth, Ramban, Rambam, Rif, Ran, even Shulhan 'Aruch, Rama, Shach and Taz - as being, really, 'Omek HaPeshat ('Iyun being much more in depth analysis than even most very serious Yeshivah students get in their first few of years of learning). 

Along similar lines, R' Cohen basically says that Rashi's idea of Peshat is to bring background to help the student understand what is going on in the Pasuk.

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Again, this is my own interpretation of R' Cohen's presentation of Rashi's approach to Parshanut. I really am not doing him any justice, but I wanted to highlight it anyway, because I think it is rather brilliant.