Turn is a time unit used to measure Battle duration. The game timer can be seen in top right at any time. All aiming seem to have certain turn costs, a shot being executed if the wait time successfully passes. In case it's not, a trooper is interrupted, having to start an action over. Apparently, weapon 
Recovery allows to draw direct comparisons of aiming times, but the theory is not consistent to tell for sure.
When a dummy is granted an 
Initiative boost, the timer advances by the value of the bonus and freezes. At the same time a blue bar appears indicating what part of the boost has been spent. When it's over, the time flows as usually.