From LQWiki

verbose: using an excessive number of words to describe something

In the computer world verbose means that the tool will give more information than usually needed.

Tools often give little to no feedback about their status or results. This is good when using them in batch processing. but when trying to fix something, using verbose mode will often help finding the problem by analysing the (verbose) output of the programs.

Getting verbose output is frequently achieved with the '-v' option, but see the specific man page for details on each tool.