A full adder Black Box has the functionality of a full adder with three inputs and two outputs. Exactly how the black box works inside, is no longer of interest to you.
With this black box you can now easily draw a full 4-bit full adder...
The carry-out bit of one digit becomes the carry-in bit to the next level digit. At the end of the calculation you get the result of the 4-bit addition plus one carry bit. This arrangement can be continued, so you can realize effortlessly 8 -, 16 -, 32 - or 64-bit full adders.
With the IC's that you bought, you can no longer build this circuit. The circuit, built up only with basic gates, would be very complicated and messy. Therefore, IC's are available containig a full adder as a "black box". A black box is therefore not just a trick on paper. In digital electronics, it is often used to simplify circuits.
But now you get to know one other important field where logic gates are used.