Initiative in YAGS is quite an important part of how the combat system works. A lot of the time, initiative defines the order in which everyone acts within a round. At the end of the round, things begin again in the same order. After the first round or two, who went first no longer really matters, since going first just means you're going after the person who went last.
Combat is split into rounds which are about five seconds long. At the start of combat, at the beginning of the first round, everybody determines their initiative using Agility × 4 + d20.
YAGS then splits initiative into two phases - declaration and activation.
In reverse order of initiative, from lowest to highest, everybody declares their action for that round. This means that people with higher initiative scores get to decide what they are doing after slower people have made their decision, which gives those with a high initiative a big advantage.
Once everybody has declared, then activation occurs, with everyone taking their action in order of initiative from highest to lowest. So not only does someone with a high initiative score get to know what slower people are doing, they get to act first as well.
So Bob may declare that he is shooting at Alice, and Alice declares that she is diving behind cover. Alice then dives behind cover, and Bob gets to shoot at… nothing because Alice is no longer visible.