alright
well let's start here, I'm assuming there's no issue with the word "media" (I hope, anyway) so the problem word for you must be "corporate" so let's take it one step at a time. we'll start by defining "corporate"
cor·po·rate
/ˈkôrp(ə)rət/
adjective
1. relating to a corporation, especially a large company or group.
"airlines are very keen on their corporate identity"
so now that we've set a foundation let's try combining the words and trying to suss out what their meaning together could possibly mean. so we've established that "corporate" is relating to a corporation, especially a large company or group. seems like the combined definition of those words would have something to do with large companies or groups being affiliated with or even outright owning a large portion of the media. since we're sussing out that meaning by using the definition of the word "corporate" paired with media we'd have to check on the validity of such a claim because just throwing around phrases like that can be dangerous. so let's do some minimal digging.
what's this?
right off the bat you've got sourced claims that in 1983 90% of the media was controlled by 50 companies but by 2012 90% of the media was controlled by just 6 companies
clicking through to the source of that claim gets us to this page
which has a helpful info-graphic about what we're talking about
so it does seem like when we defined the problem word "corporate" for you paired with the word "media" we did indeed land on the correct definition of the phrase "corporate media" and now you should have a better understanding of what that means and why it might be seen as problematic especially for those who are concerned about the staggering amount of inequality in regards to power and wealth the few have over the many, which the corporate media is emblematic of and is an active participant in proliferating
hope that helps and as always bring that knowledge forward with you on your endeavors
