It can be used to increase the condition of the currently equipped weapon, up to a maximum of 100%. Earth weapons are extremely rare aboard the ship, so the epoxy is the only alternative to repair weapons brought aboard. The percentage repaired depends on the user's Repair skill:
Alien epoxy comes in tubes and over 100 tubes can be found in Mothership Zeta. Since they have no weight, all tubes found can be carried without being over-encumbered. While the effect of one tube may not conform to the table above, it is always possible to increase a weapon's condition to 100% by applying multiple tubes consecutively, regardless of a player character's Repair skill. Alien epoxy cannot repair armor or clothing.
Alien epoxy cannot be applied in the repair menu. Rather, it can be found in the "Aid" section of the Pip-Boy and used like any other consumable to repair the currently equipped weapon.
The weapon must be equipped in order for the epoxy to repair it. Therefore, alien epoxy cannot repair completely broken weapons.
Upon completion of Mothership Zeta, talking to Sally every 24 hours will yield a random item, which could be alien epoxy.
Behind the scenes
An "epoxy" is a step-growth thermoset polymer that solidifies around the applied area, such as glue.