All analogue electronics generates some level of noise, and digital recordings also introduce a small amount of dither noise in order to accurately record signals.
When you record sound from a microphone, you are recording the person speaking, but also the sounds present in the room, the indirect sound of the person speaking reflecting off the objects in the room, and the noise associated with the analogue and digital systems being used.
What we're listening for is the ratio between the desired signal and the undesired noise. Generally when recording with high quality microphones (like the U87) and a good pre-amp, noise is likely to be introduced by poor microphone placement, the wrong directional pattern being used on the U87, or recording levels being too low at some point within the signal chain before the audio is recorded.
U87s have a directional pattern setting which can change the response of the mic between omni, cardioid, and figure of 8. In an echoey room with no acoustic absorption, a recording of a person speaking in front of the mic set to a 'cardioid' pattern will have a greater proportion of direct to indirect sound recorded. The trade-off is that 'figure of 8' and 'omni' have slightly better frequency response patterns.
Even if you recorded in an anechoic chamber, there would be no room noise, but there would still be noise caused by the analogue and digital circuitry. If your gain is set too low on the pre-amp or any other gain module before the signal is recorded, an undesirable level of noise would be introduced to the signal path. If the digital level that you record at is set too low, you will also be introducing more noise into your recording, as the ratio of your signal to the quantising and dither noise introduced by sampling the signal digitally will be worsened.
Practically speaking, your audio clip doesn't sound that bad to me. You could try noise reducing the recording using Adobe Audition's built in noise reduction tools. You could re-record with your subject closer to the mic (but they sound pretty close mic'd already given the amount of mouth noise), and you could check your recording levels throughout your signal chain.