To give an answer a bit more technical than the others, theoretically a encryption scheme is considered fully homomorphic if it can support an arbitrary number

To give an answer a bit more technical than the others, theoretically a encryption scheme is considered fully homomorphic if it can support an arbitrary number of additions and multiplications on its inputs (bits or integers). In a lot of fully homomorphic encryption (FHE) schemes bits are represented through big matrices that are in part random and part deterministic. You can add and multiply these matrices and it will naturally add and multiply the encrypted bit inside as well, but you need the secret key to decrypt the matrix and learn if it contains a one or a zero. From these operations (add and mul) you can create a NAND gate using the formula 1 - A * B (assuming A and B are matrices containing encrypted bits) and create any arbitrary boolean circuit from there. These circuits works on the encrypted data without the need to decrypt it. (there is an additional step called bootstrapping that most schemes require in order to allow circuits of unlimited depth but I won’t get into that in such a short answer)