Neutron flux is the term used to describe the amount (
number, really) of energetic neutrons passing through an area over a given amount of time. This is particularly useful in describing areas near significant neutron production; when building a
nuclear reactor facility, knowing the neutron flux of all the personnel-occupied spaces is critical; on the other end of the size scale,
high energy weapon designers must cope with areas of high neutron flux within the devices itself. The former has
deleterious effects on people; the latter has nasty and potentially unpredictable effects on the components of the weapon. This can cause problems ranging from simply radioactivity of components, causing hazard to service techs, all the way to
malfunction of components (especially
electronic ones) and either failure or (worse) premature
activation of the device.
Neutrons are classed as ionizing radiation, which means they pose a double threat. They may cause damage themselves, by stripping electrons and breaking bonds; they may also cause substances they interact with to become unstable (i.e. radioactive) which in turn cause later harm. Keeping close tabs on the neutron flux of your design, or your personnel quarters, is extremely important.
One caveat: the term 'flux' in other physical uses tends to imply a differential across a volume. For example, a thermal flux means that heat energy is passing through the volume due to a gradient between the edges; heat is moving from the hotter area to the cooler area, as required by thermodynamics. In the case of Neutron flux, however, the value is consistent across the area since neutrons are not induced to move by local physical conditions. The particles themselves have energy, expressed as motion, and that is what determines the direction and destructiveness of the flow.
Damn it, Custy, tell me something useful! Okay. The neutron flux is expressed (typically) in φ, which is defined as n/cm2/s, or the number of neutrons (n) passing through an area of 1 cm2 at an angle normal to their direction of travel. Think of it as making a ring of your fingers in a rainstorm, the flat of the ring facing up. Assuming no wind, the 'neutron flux' would be a count of the number of drops per second that passed through your fingers.
There's naturally all sorts of screebling nasty math that goes with this which I will spare you (mostly because I have but a tenuous grasp of it myself). The subject holds my interest as a defense geek, where it turns up in reports and studies detailing (for example) the reasoning behind the creation of the enhanced radiation weapon (neutron bomb).