Turn is a time unit used to measure Battle duration. The game timer can be seen in the top right throughout the battle. Aiming of a weapon seems to have certain turn costs. A shot being executed if the wait time successfully passes. If not, trooper will be interrupted and will have to start the aiming action again. Apparently, weapon Recovery allows one to draw direct comparisons of aiming times, but the theory is not consistent enough to tell for sure.
When a trooper is granted an Initiative boost, the timer advances by the value of the bonus and freezes. At the same time, a blue bar appears underneath the timer indicating what part of the boost has been spent. When it's over, the time flows as normal.