Some people call it phrasing. I also like to think of it as line, because lines show shape, and musical ideas are made of lines of different lengths and thickness that interact with one another.
As a flute player I always envied oboe players. Their supply of air could last for pretty much as long as they wanted it to, allowing phrases in Bach, for example, to reach their points of repose after following very long musical paths. Flutists, who have to waste half of their air supply making a sound, often have trouble developing the intellectual ability to think in long phrases because they lack the physical ability to execute them. There are exceptions, like Emmanuel Phaud, but they are exceptional. I always hoped that playing with real musical line and being able to allow music to develop in really long phrases would be something I would gain with age and maturity. For me it took more than age and maturity; it took learning to play instruments other than the flute, and to experience the mapping of phrase lengths in repertoire other than the flute repertoire. And even with age and maturity (now that I'm 50), the struggle to keep track of long phrases, and carry them, like tea trays, to their various destinations (which are sometimes difficult to determine) is constant.
The other day I watched a television broadcast of a concert I played last weekend. There was a very young pianist playing the Tchaikovsky Concerto who played with true musical line. I'm grateful for the broadcast because there was a great deal I wasn't able to hear because I was playing myself.
This pianist's sense of musical line--getting from one note to the next, or from one note to an important one that happened to come a measure or two later--was extraordinary. He must have been thinking about his phrasing all the time because there was nothing accidental or casual about the direction of any phrase. But, in spite of his tremendous control, every phrase was surprising and compelling. The one-note-to-the-next progress of the piece was as important as the one-phrase-to-the-next progress. And that was just the skeletal level of the piece. On top of the beautiful phrasing, everything was dressed in an array of brilliant musical colors. It was very inspiring, partially because his musical choices seemed so completely natural.
So, I have been working on trying to keep track of long musical lines, and paying a lot of attention to their sense of contour and consequence. The process of doing so, particularly when playing Bach, is kind of like following a complicated line of reasoning, while at the same time allowing yourself to be immersed in the emotional flow of everything that does not concern the intellect.