As per wiki on the Third Doctor (of Doctor Who):
The catchphrase most associated with the Third Doctor's era is probably "reverse the polarity of the neutron flow". The phrase was Pertwee's way of dealing with the technobabble that he was required to speak as the Doctor. He wanted something all purpose and easy to remember instead of myriad made-up dialogue, and Terrance Dicks provided him with the phrase.
Many fans of the show believe that it is scientifically impossible to reverse the polarity of a neutron flow. In actuality, it is possible for neutrons to flow (1) and, since neutrons have a magnetic moment(2), it is possible in theory (although difficult in practice) to have a stream of neutrons polarised along or against their direction of motion. Given this, such a polarity could presumably be reversed. However, the phrase is still meaningless in the contexts in which the series (Doctor Who) uses it.
1) Neutron Flow - http://en.wikipedia.org/wiki/Neutron_transport
2) Magnetic Moment - http://en.wikipedia.org/wiki/Magnetic_moment
-- MAKING IT SIMPLE --
-- Neutron Flow --
To simplify to my basic understanding, the "Neutron flow" refers to a beam of neutrons moving AWAY from a neutron-generating point/source.
Unlike electricity which requires two poles (positive and negative), a Neutron Flow operates (in a sense) more like a monopole: it has a source, a stream of neutrons moving away from that source, and an eventual negation/alteration point (where the neutrons are absorbed, re-combined, split, or has its SPIN or Rotation-speed altered). A neutron flow doesn't need to follow a specific linear-path (like a wire) from one pole to the next. It can be a free-floating point inside an orb (like a sun within a dyson sphere).
-- Polarity on the Flow --
And while you can argue that they aren't magnetic (since neutrons are neutral), you can argue that they can "spin" since they are indeed particles. This means the "neutron flow" CAN HAVE a magnetic-like feature... spin them one way and you have something like the typical electro-magnetic effect.
The How: the left-hand rule of electron spin and travel direction. Neutrons moving away from a source all with one spin direction would be considered "negative" if they obeyed the typical left-hand spin-travel part of the electron rule... and "positive" if they spun the other way.
So if in a beam, so long as all neutrons spin in one particular direction, the "neutron flow" can have a negative (electron-like) spin or a positive (anti-electron) spin.
-- Thus you can have "a polarity" on the "neutron flow" ---
And thus you can also "reverse the polarity on the neutron flow". Though unlike an electron flow, where this would mean the electrons are going the opposite direction, the "reversed neutron flow" would still be moving in the same direction as before... it would just be the "spin" of those neutrons is reversed.
-- Practical applications --
Unknown at the moment. Though I could guess that from a particle point of view, hitting a spinning object can vastly alter the resulting trajectory. Whether this could have a useful effect (like say, controlling gravity or creating artificial gravity) or who knows what (tuning the exact phase of warp plasma? some other techno-babble?)