"High crimes and misdemeanors" is a phrase from Section 4 of Article Two of the United States Constitution: "The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors."
Let's take a look at the entire phrase. It starts by listing Treason and Bribery, and then adding other high crimes and misdemeanors. In this context, the term "other" can only mean "similar." (Otherwise, there is no need or meaning for that term.)
Thus the "other" high crimes and misdemeanors means those of similar seriousness to treason and bribery. To claim that impeachment is nothing more than a legislative popularity contest is to ignore the specific wording of the Constitution which authorizes this procedure in the first place.