In my snotty nosed "yoof" period at Locking I seem to remember this little gem being called a Balun. (Of which there are at least 4 different types).
Used where the RF half wave characteristics ( λ/2) of the antenna are not correctly matched to the impedance of the coax or transmission line. Some transmission or reception loss occurs but if correctly calculated and tuned can reduce the losses to approaching 1/1.