To “tap [a permanent] for mana” is to activate a mana ability of that permanent that includes the {T} symbol in its activation cost. See rule 605, “Mana Abilities.”
May 3, 2019 · War of the Spark
One card (Drain Power) causes one player to lose unspent mana and another to add “the mana lost this way.” (Note that these may be the same player.) This empties the former player’s mana pool and causes the mana emptied this way to be put into the latter player’s mana pool. Which permanents, spells, and/or abilities produced that mana are unchanged, as are any restrictions or additional effects associated with any of that mana.
January 25, 2019 · Ravnica Allegiance
One card (Drain Power) causes one player to lose unspent mana and another to add "the mana lost this way." (Note that these may be the same player.) This empties the former player's mana pool and causes the mana emptied this way to be put into the latter player's mana pool. Which permanents, spells, and/or abilities produced that mana are unchanged, as are any restrictions or additional effects associated with any of that mana.
April 27, 2018 · Dominaria
One card (Drain Power) causes one player to lose unspent mana and another to add “the mana lost this way.” (Note that these may be the same player.) This empties the former player’s mana pool and causes the mana emptied this way to be put into the latter player’s mana pool. Which permanents, spells, and/or abilities produced that mana are unchanged, as are any restrictions or additional effects associated with any of that mana.
January 16, 2016 · Oath of the Gatewatch
One card (Drain Power) puts all mana from one player’s mana pool into another player’s mana pool. (Note that these may be the same player.) This empties the former player’s mana pool and causes the mana emptied this way to be put into the latter player’s mana pool. Which permanents, spells, and/or abilities produced that mana are unchanged, as are any restrictions or additional effects associated with any of that mana.