A cost arrow icon (→) can be found in the description of player cards. In ability text it distinguishes a cost from an effect. Read as in “pay cost → resolve effect”. Nonbolded text before the cost arrow icon must be paid and/or resolved in full before the text after the cost arrow icon can be resolved.
Let’s take Avengers Mansion as an example “Exhaust Avengers Mansion → choose a player. That player draws 1 card.” First we exhaust the Avenger Mansion, then we pick a player and that player draws 1 card. If the Avenger Mansion is already exhausted, the cost can’t be paid, so you can’t get the effect.
Q. Can I use Captain Marvel’s hero ability if I’m full health?
A. If you are full life, you can’t pay the cost, therefor you can’t use Captain Marvel‘s ability Rechannel.
