Broad spectrum refers to sending a radio signal over a broad spectrum of frequencies. Very early spark gap transmissions were actually broad spectrum, because their transmission radio frequency was sent over a wide bandwidth (2). However, as technology progressed, radio waves were sent over specific frequencies. Radio stations still use this method today, because you tune the radio to a specific station depending on what you want to listen to (3).
Radio transmissions proved over specific frequencies proved to be a problem for military communications, because the transmission could be easily jammed (4). The Allies during World War II ran into this problem when their radio transmissions (including the jamming of signals to radio controlled torpedos) were being jammed by German submarines (4).
Frequency hopping is when the signal is transmitted in short bursts, and jump between a set of predetermined frequencies (3). This makes figuring out the signal and jamming it much more difficult. While Hedy Lamarr is often credited with inventing frequency hopping, there were other people who had similar ideas previously. Germany during World War I used a type of frequency hopping to prevent their transmissions from being picked up by the British (5).
Frequency Hopping Diagram (credit)