If you decide to pledge your final loyalty to the Brotherhood of Steel Faction in Fallout 4, then you will no longer be able to complete quests or contact allies of other factions. Both the Railroad and The Institute will be permanent enemies. You will be sent on several missions that enable you to wipe out the entirety of the Railroad and the Institute. So be prepared and save your game before jumping into this ending!
You will infiltrate the Railroad's hideout alongside the Brotherhood of Steel and wipe out the remaining members. You also have a quest where you raid the location of The Institute. But in order complete this quest however, you will need to help the Brotherhood complete a 40-foot robot named "Liberty Prime." to aid in the assault.
Afterwards, you will meet up with Elder Maxon on top of a building that sits really far away from the location of The Institute main HQ. Elder Maxon gives you the honor to press a button, which will set off the pulse charges that are planted inside the building. A nuke will explode and kill any living thing inside of it, as well as disable any entrance into The Institute location itself.
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At the very end, you will get promoted to the rank Sentinel in the Brotherhood of Steel. You also gain a jetpack for your Power Armor. Everyone that is part of the Brotherhood of Steel will also have a great deal of respect for you in their dialogue, as well as appear in various locations like Diamond City!
Other endings
You can check out the other endings here!