According to Mr. Fournier's Wikipedia page... He's known for being the "aristocrat of cellists, on account of his elegant musicianship and majestic sound." Virgil Thomson wrote in the New York Herald Tribune, "I do not know his superior among living cellists, nor any...who give one more profoundly the feeling of having been present at music-making." Read more here.
The thing I love most about Mr. Fournier is his posture while playing. (Go ahead and roll your eyes...) Seriously, if you watch him, you'll see his shoulders totally relaxed. His arms curved around his cello... Oh wow it's good. You can see by his playing, why he was a teacher for most of his life.
Another thing I find interesting to note, is the frequency of his vibrato. I find it fascinating to consider the trend of popular singers' vibrato at the time of the height of his playing... the trend for a wide, rapid warble must have bled into Mr. Fournier's fingers.
Just so you know, Pierre Fournier is my favorite recording of the Bach Suites... :-)