What does thrust and thrust axis mean in particle physics? Would someone be kind enough to explain to me:
1) How thrust and thrust axis are calculated/determined 
2) What is the significance/interest in these quantities for an event in particle physics? 
Though I have seen the general formula, I haven't found a good explanation of what it tells you about the event or why it is useful. 
 A: Sphericity and thrust came into being when scattering experiments demonstrated that the parton model of particle physics could not explain the data, that there was a type of "hard core" giving tracks with  high p_transverse. The need arose to be able to orient the individual events in a way that would demonstrate the emergent jet structure.

Spear (SLAC): mid-70’ies, e+e− → qq should have 1 + cos2 θ angular distribution if quarks have spin 1/2.
Solution: Sphericity.
Fixed-target pp experiments study alignment of collision.
Solution: Thrust.

The thrust  variable characterizes the event shape: an event with spherically distributed tracks would have Thrust =1/2, a two jet event would have close to 1.

It is a variable which can be calculated phenomenologically in QCD  and compared with the data and was important in establishing the correspondence of the jet structures to the quark and gluon content of the interactions.
See also Why is the value of thrust for a perfectly spherical event equal to ${\frac{1}{2}}$? for the calculation.
