Performing an interference is done by playing a card during an opponent’s turn to hinder or cancel an action they are taking. This is traditionally done through the use of Command cards, as they can be used at any time, but there are abilities that exist that can act as interrupts. If you and your opponent respond to eachother’s interrupts, then each card ability resolves in the order from the last card played to the first card played.  Consider this example:

Player 1 has a Rumia on the field.
Rumia is only a 3/2

- Player 2 uses an ability to to deal 2 damage to Rumia
- Player 1 uses a card to give +1/+1 to Rumia
- Player 2 does not respond further

If Player 1 chose not to respond to Player 2’s damaging ability, their Rumia would have been destroyed. However, because Player 1 interrupted and gave Rumia +1/+1, she survives through this ordeal.