Origin and developpement of the term "HAM Radio"
"HAM" is an informal notion for "Amateur Radio Operator" and in the broad sense of the term for Amateur Radio in general. The notion first appeared sporadically in the early 20th century in the USA. He found a wider circulation only around the 1920s in the English-speaking world.
The etymological origin of the term
It is obvious that the expression "HAM" in amateur radio language does not mean ham on the bone!
One reason for the hesitant use of the term HAM is probably the fact that it was a pejorative expression of the jargon of the long distance telegraph operators of the time and meant "bad telegraphist" .
At the beginning of the radio era - it was wireless telegraphy in this case-, there were still a great number of professional morse telegraphists on wireless telegraph networks. When the first amateurs appeared on the air, they were scornfully called "HAM" by professional telegraphists who dismissed them as "clumsy" .
Little by little, the word HAM has become a replacement for the word "Amateur Radio" and more and more amateur radio operators have adopted it with pride as the designation of their hobby. Thus, a pejorative term of origin has, over time, become a universally known and honorable notion, especially in the English-speaking world.
There are still other interpretations that are, however, hardly likely.
 McClure's Magazine, January, 1902, page 231 : L. C. Hall, “TELEGRAPH TALK AND TALKERS”, Human Character and Emotions an Old Telegrapher Reads on the Wire, The Slang of the wire