You can obtain different trophies by fighting bosses.
The maximum bonus % that trophies give:
15% to resource production
100% to village strength
70% to army attack and defense
70% to units' capacity
50% to units' training speed
65% to construction speed
Trophies do not drop in any specific order. This means that if you already posess a trophy for a N% improvement you may get a trophy with a lesser rate.
In order to activate trophy bonuses, you need to install them in a Tavern.
Regards, Nexters Support Team