You first main mission goal on reaching Manhattan is to get to the Base of Operations. This is located in the James Farley Post Office a short sprint from Camp Hudson where you initially arrive.
This is a Safe House for you with mission boards / givers, Vendors and resupply crates. It also serves as a hub for the main mission series in the game. Unlike other safe rooms though this is not a public area. It is for you only.
The BoO has 3 wings (Medical, Security and Tech) which you will be tasked with activating and upgrading by completing mission throughout the city and collecting supplies. Each level of the wings that you upgrade and activate will unlock Talents, Skills and Perks for your character.
To activate each wing you will need to assist / rescue the a key person to run it. Once they return to the BoO the wing is set up and you are able to begin unlocking the various areas and restore the base to full working capacity.
At the entrance to the BoO you will find a status board with your progress through each wings activtation shown.
The BoO has Weapons, gear, and mods Vendors to buy Gear from .The gear available will always be in your current level range. There is also a special vendor found at the back of the corridor opposite the main entrance. This is the Rewards Claim Vendor. If you have any items that you are owed as part of a pre-order bonus. Or from owning other related games then this is where you can pick them up.
The Crafting station lets you create Weapons and gear from parts and supplies found around the map. You can also get the components by breaking down items in your inventory.
The stash box is for you to store items that you want to keep but don't want to maintain in your Backpack. Good for the hoarders amongst us who want to hold on to interesting but not very useful items and not run out of space in your inventory. If you create multiple characters it will also be a place to share items as they will all have access to the same stash.
It is also the place that Dark Zone gear will appear in after you have successfully extracted it.