The two main functions are safety and shielding.
Most transformers and chokes have high voltages, and the windings are protected only with paper and possibly a strip of fabric. Often there are also exposed metal terminals. The bell makes these voltages less accessible - which is also why it should be grounded!
Transformers and chokes are used with AC voltages, either power line or audio. These can couple capacitively to or from other parts of the circuit, resulting in crosstalk, hum, instability, and other nuisances. The coils are often designed to minimize the radiated field, or the sensitivity to fields from other sources, but this is not always good enough. In that case, the end bell shields the coil form the rest of the circuit.
