The Monument Building allows you to activate Insignia that give a temporary extra boost.
The Monument is one of the special buildings that needs to be unlocked before you can use it. You can unlock the Monument by purchasing any pack after first having upgraded your Headquarters to level 3. The Monument building is located to the left of your Headquarters.
By clicking on the Monument you get into a screen where you can activate one of the Insignia you possess. You can select an Insignia by clicking on the empty icon in the left middle of the screen.
Each Insignia has its own specific boost, duration and cooldown timer. Once you activate an Insignia you cannot use it again until the Cooldown timer has expired.
Like with materials there are 6 different quality levels of Insignia and you can combine the lower level to higher level in the Armory. However, I have yet to see a lower level Insignia, all of the ones I have come from packs and are Gold/Level 6.
There are a wide variety of different Insignia and new Insignia are released regularly with new or increased boosts.
The Building Development research tree contains a 2nd Insignia Slot project that allows you to unlock a 2nd Insignia Slot so that you can activate two Insignia at the same time.
It gives some nice boosts, but at this stage nothing too significant compared to other ways in which you can acquire boosts. Since you do not have to upgrade this building, just see what Insignia you already have or get in packs you would have purchased anyway.