From The Gospel of Mark by Mary Healy, comnenting on Mark 10:45:
The passage concludes with one of the most important sayings in the Gospel, summing up the purpose of Jesus’ messianic mission: For the Son of Man did not come to be served but to serve and to give his life as a ransom for many. Jesus’ own coming into the world (see 1:38; 2:17) was not for the sake of any advantage to himself, but only to serve his heavenly Father and all men and women. Here he explains that this service entails giving up his life as a ransom. The idea of a ransom expresses a price that is paid on someone’s behalf; for instance, to free a slave (Lev 25:51) or to save someone whose life is in jeopardy (Exod 21:30). God is often said in the Old Testament to have ransomed his people from slavery in Egypt or exile in Babylon (Deut 7:8; Isa 35:10), and the Jewish hope was that God would definitively ransom his people from sin and death (Ps 130:7; Isa 59:20; Hosea 13:14; Luke 24:21). The Old Testament never clarifies how God could be said to “pay a price” for his people; only in the passion of his Son does the price become clear. “For” many can mean both “in place of ” and “on behalf of ” many. Though we have nothing to give in exchange for our life (Mark 8:37), Jesus can give his own life, a gift of infinite value, in exchange for us. “Many” is not intended to exclude some, as if Jesus did not die for all (Christ “gave himself as ransom for all”; 1 Tim 2:6); it is a Hebrew way of expressing a vast multitude. The saying alludes to the Suffering Servant in Isaiah (Isa 52:13・53:12), who “gives his life” as an offering for sin that is, a sacrifice that atones for sin on behalf of “many.” St. Paul further developed this insight into the meaning of Jesus’ passion (Rom 3:24; 1 Cor 7:23; Gal 3:13; 1 Tim 2:6), which became a crucial part of the Church’s theology of redemption.