How offering up your suffering, helps those for whom you are praying...
The Eternal Truth said to St. Catherine of Siena: "I will pardon both sin and punishment in those who humbly and reverently accept the teaching of my servants. How?" They will receive grace to truly know and regret their sins. And the more that they accept this grace, the more they will receive, but if they are not willing, they will receive less grace.
"I am saying that through your desires they will receive both forgiveness and its gifts, unless their stubbornness is such that they despair. (Then I would reject them for scorning the blood by which they have so tenderly been bought.)
"What fruit do they receive? Pressed by my servants' prayers, I look on them and give them light. I rouse the dog of conscience within them. I make them sensitive to the perfume of virtue and give them delight in the fellowship of my servants. Sometimes I allow the world to show them its true colors, letting them feel all sorts of emotions, so that they may know how inconstant it is and be more eager to seek their homeland of eternal life. The eye cannot see, nor the tongue tell, nor can the heart imagine how many paths and methods I have, solely for love and to lead them back to grace so that my truth may be realized in them!"
St. Catherine of Siena, The Dialogue, Translation by Suzanne Noffke. O.P.,(Paulist Press, New York)