The Local Interstellar Cloud (LIC) or "Local Fluff", is the name of the cloud of dust that the solar system happens to be passing through at the moment. The LIC is about 30 light-years across, and we have been within it for tens of thousands of years. There are a number of these clouds in the Local Bubble, and we are actually rather near the boundary of the LIC, and may be entering the neighboring G-Cloud in the next 10,000 years or so.
The Local Bubble is a low-density area in the interstellar medium, which consists of the residual gasses of ancient supernovas. Even so, the LIC is even lower density, a wispy mixture of hydrogen and helium atoms which would be overwhelmed by these surrounding higher density (but also very, very wispy) gasses if it were not magnetized; the LIC has a magnetic field of 4 and 5 microgauss. It is estimated that its velocity is 26 km/s, and that its overall density is about 0.264 atoms per cubic centimeter. It is also quite hot, with a temperature of 6000 C; however, the individual atoms are spread so thin that this heat would have a negligible effect if we were to interact directly with the gasses.
The solar system is protected by the sun's heliosphere, which deflects most of the interstellar wind. However, that which does make it through the heliosphere, a very small amount of helium, is bent by the sun's gravity in such a way that that the Earth passes through this wind from November 30th to December 17th, giving us a short period of time to analyze 'samples'. Even so, it wasn't until 2009, after Voyager exited the heliosphere, that we were able to determine that the LIC had its own magnetic field.
The nickname 'Local Fluff' has caught on among astronomers, and is often shortened to simply Fluff. This terminology is common enough to appear in NASA press releases and popular science articles; while this is certainly not a formal term, it has completely replaced the term "Local Interstellar Cloud" in at least one of NASA's news releases, somewhat ironically as an attempt to avoid technical Jargon.
References:
NASA: IPOD: The Local Interstellar Cloud (map)
NASA: APOD: The Local Bubble and the Galactic Neighborhood (map)
NASA: Voyager Makes an Interstellar Discovery
NASA: A Breeze From the Stars
NASA: Sheilds Up!