Broscience is apparently a term that's become more popular amongst the not-particularly-buff-but-into-bodybuilding crowd, to refer to any knowledge or wisdom that does not comport with their current, trend-based understanding of nutrition, training and supplementation.
Broscience is basically a term in skinnier people use an attempt to sound more knowledgeable about a topic, but what they fail to understand is that their reasoning is typically at least as equally flawed, and for the same reasons, as what they are criticizing.
For example, a guy may say that taking amino acids while training is unnecessary, and constitutes "broscience."
Why? Well the latest studies to come out apparently show this to be the case, and it is now trendy on bodybuilding boards to denounce taking amino acids while training as "broscience."
However, the idea of taking amino acids while training was probably brought forward in the past by other studies as well as anecdotal experience, which may contradict current studies and anecdotal experience.
Point being, studies contradict each other all the time, so anecdotal experience has a type of legitimacy that scientific studies can't completely replace. In 5 or 10 years, new studies may again show the value taking amino acids while training, and the trend while shift again.
Therefore, by their own definition for broscience, most of those using the term are in fact engaging in broscience themselves.
This is based on something I read recently on a popular bodybuilding board.
Guy on BBing board who by admission weighs 140lbs: "Wow that guy (who has trained 17 Olympic atheletes, has worked with numerous professional sports teams, and himself weighs 210+) recommends large amounts of BCAA's while training?! What an idiot! Everyone knows that BCAAs while training is just broscience!"