Training size, squad size, training speed, and unit production bonus are all in-game terminology.
Squad size: The number of troops per squad (troops being unit size * number of units).
Training size: The number of troops that can be allotted to a production slot.
Training speed: The number of troops that can be trained in 12 minutes (not including unit production bonus).
Unit production bonus: The amount of extra troops picked up upon collection.
The only oddity is that unit production bonus is part of the total to obtain training size. So a higher unit production bonus does indeed increase your troop production and training size, but increasing armories merely increases training size without increasing troop production.