The orbit of a satellite about the Earth (or anything else, for that matter) is in the shape of a conic section, with the center of the Earth at one focus of the conic section.1 The orbit, therefore, lies in a single plane in space, which also contains the center point of the Earth.
The Earth's equator also lies in a single plane in space, containing the center point of the Earth.
These two planes, the orbital and and equatorial, intersect in a line passing through the center of the Earth. This line is called the "node" of the orbit.
The node line is often depicted as two vectors, separated by 180 degrees, pointing away from the Earth's center along the node. The ascending node is the vector intersected by the orbit as the satellite moves from south to north. The descending node is the opposite: the vector intersected by the orbit as the satellite moves from north to south.
One of the six classical orbital elements2 is the right ascension of the ascending node (Ω). Ω describes the angle in the equatorial plane between the ascending node and the vector Î, which points from the Earth's center to the vernal equinox. In older books, Ω is sometimes called the longitude of the ascending node - this is incorrect; it is not a longitude. Ω is sometimes, in shorthand, referred to simply as the "node"; it should usually be clear from context whether "node" refers to an angle (Ω) or a line (the intersection of the two planes above).
1Orbits come in elliptical, circular, parabolic, and hyperbolic shapes. Since these are formed by the intersection of a cone and a plane, they each lie in a single plane.
2Six elements are required to completely describe the state of an orbit. There are many different sets of these elements. The "classical" (or Keplerian) elements are among the most intuitive of these, and consist of the semimajor axis (a), the eccentricity (e), the true anomoly (ν) (that's a nu), the inclination (i), the right ascension of the ascending node (Ω), and the argument of perigee (ω).
In finite element modeling, a body being acted upon by a force is divided up into many segments (elements). In each cross-section thus revealed (that is, on each end of each segment), a single point is chosen for the purpose of analysis. This point is called a node.