"High" in the legal parlance of the 18th century means "against the State". A high crime is one which seeks the overthrow of the country, which gives aid or comfort to its enemies, or which injures the country to the profit of an individual or group. In democracies and similar societies it also includes crimes which attempt to alter the outcome of elections.
The first impeachment conviction by the U.S. Senate was in 1804 of District Judge John Pickering for the high crime and misdemeanor of chronic intoxication. Federal judges have been impeached and removed from office for tax evasion, conspiracy to solicit a bribe, and making false statements to a grand jury.