I am interested in the terminology of the following words: baseband, broadband and bandwidth applied in tellecomunications. What is the meaning of the words, how were they formed and what do they mean in the context of modern networks?
"Band" applies to the range of electromagnetic spectrum used for the transmission.
Broadband uses a broad range (as opposed to narrowband), baseband is a band starting at zero frequency (or close to).
Bandwidth is used for both the spectral width of a band or channel (e.g. "100 MHz") and for the amount of data that can be transported in a given time frame (as in "100 megabytes per second"). The data throughput meaning is borrowed from the original, spectral meaning - partly because they are correlated.