Communion of saints is an important theme in the Pauline letters, particularly 1 Cor 12 where St. Paul teaches that "we were all baptised into one body" (1 Cor 12:13) in one Spirit, and in this one body "if (one) part suffers, all the parts suffer with it; if one part is honored, all the parts share its joy" (1 Cor 12:26). In the Eucharist, all members of the Church partake of the bread as one body in communion: "The bread that we break, is it not a participation in the body of Christ? Because the loaf of bread is one, we, though many, are one body, for we all partake of the one loaf" (1 Cor 10:16-17).
After narrating the faith of many ancient saints down the line of salvation history, the author of Hebrews concludes: "Therefore, since we are surrounded by so great a cloud of witnesses, let us rid ourselves of every burden and sin...while keeping our eyes fixed on Jesus..." (Hebrew 12:1-2). Note that he uses present tense - "we ARE surrounded" - in referring to the presence of these ancient witnesses to our faith. And understandably so because we ARE in communion with them.
The communion of saints concept is also illustrated beautifully by Jesus himself in John 15 using the motif of vine and its branches. Every member of the body benefits from Jesus - the Head of the body (Eph 5:23). With us dwelling in him, and him in us, it gives us life - abundant life (John 10:10) - the way the vine gives water and nutrition to its branches. By virtue of our communion in the body of Christ, there's NOT A MOMENT we don't benefit from Christ and, as St. Paul teaches in 1 Cor 12:26, from the other members of the body.
As members in communion with each other in the one Mystical Body, we can intercede for one another. Among all members of the Mystical Body, Mary, the Mother of the Church (John 19:27), is particularly powerful in her intercession, as was demonstrated at the wedding in Cana where Jesus performed his first miracle by turning water into wine on the prompting of his mother (John 2). But wait! Isn't Jesus "the only Mediator between God and the human race"? (1 Tim 2:5) How can a teaching that endorses multiple mediation be scriptural? Correct. This is why whether the intercession is by ordinary members like us, or by the saints in heaven, or by Mary, its efficacy is derived not from the intercessor's own merit but from sharing in Jesus' one mediation in a subordinate way.
Inevitably we have to ask a very Protestant question: In that case, why bother? Why through Mary and the saints? Why not go to Jesus directly who is the ONLY Mediator? Isn't it his mediating power the source that Mary and the saints draw on anyway?
I like St. John Paul II's answer in this regard (see Fr. Michael Gaitley's 33 Days Morning Glory, day 27). Yes, Jesus definitely could have saved us directly without going through Mary. But the fact of the matter is: he chose to do so THROUGH Mary by entrusting his body to her womb! He entrusted his infancy to her maternal care; he entrusted his childhood and youthful years to her guidance and upbringing; and on the cross, he entrusted his Church to her (he made her the Mother of his Church), wanting her to take care of the Church - his Mystical Body - the way she took care of his human body when he was growing up! So yes, we want to go to Jesus directly. But Jesus told us to go to Mary! It's not that Jesus cannot mediate directly, but that he knows we can benefit from his mediation better through Mary and the saints.
This is no different than God choosing to manifest his glory and power through his creation (Rom 1:19-20, Ps. 19:2-5). Always a good teacher who knows our needs and limitations as human beings, God uses intermediaries that enable us to understand his truth better and receive his grace more effectively.
I think this last point is very important because so many Catholics struggle because of it. To whom should we pray? Jesus or Mary? It's as though the two were in competition with one another. Of course we pray to Jesus. But we can pray with and to Mary too (CCC 2679). Mary is a great gift from Jesus (again John 19:27) that's meant to help us, to bring us closer to Jesus. We shouldn't hesitate to use Jesus' special gift for us. Mary doesn't compete with Jesus. She is his coworker, assisting him to sanctify us the way she assisted him in realizing the incarnation and the economy of salvation.