The F-function in the Blowfish Cipher is a crucial component of its encryption process. It operates on half blocks of data, dividing them into four 8-bit quarters. Each quarter is used as an index into one of the four S-boxes (substitution boxes), which are initialized during key setup. The outputs from these lookups undergo bitwise operations: XORed together and added modulo 2^32. This result forms the output of the F-function, contributing to the cipher’s overall security by introducing nonlinearity and confusion.