"Go'eil" is usually translated as "redeemer." That definition rings true and meaningfully for Christians, for whom redemption is a central and constant concern. But I think it is sometimes hard for Jews to understand what exactly we mean by the term.
Go'eil has three connotations (and translations). The first is someone who rescues someone from danger or oppression. In that sense, we would probably translate the word as "savior." That term has deeper religious connotations than it is meant to have. Outside the context of religious life, however, savior and rescuer mean essentially the same thing.
The second meaning is that of someone who pays the price in exchange for something held captive or prisoner. In more benign contexts, use "redemption" to refer to frequent flyer miles, thank-you points or, in days gone by, S&H Green Stamps. By turning in the evidence of credits, we can take away an airline flight, an I-pod or a toaster. In this context, however, the go'eil, the redeemer, is the one who pays the ransom for a captive human being.
The third meaning of go'eil is "avenger." In the Torah, the word is sometimes paired with "blood." The person called "go'eil hadam," the blood avenger, is the relative given the right to kill a manslayer (who can escape only in a city of refuge). In this meaning, the go'eil is presumed to have a right to seize payment on behalf of a victim unable to seek redress him- or herself.
Two things should be noted when this word appears in our prayers. The first is that there is a presumption that we live in circumstances that demand a savior, redeemer or avenger. Our liturgy posits that we are somehow oppressed, captive or wronged – and powerless to correct those situations ourselves. Given the development of the prayerbook during the long centuries of our disenfranchisement from our homeland and host socieities, it is an understandable mindset.
The other is that our prayers affirm that God will "bring a redeemer." Someone presumably human will serve as God's agent of redemption, someone that God will escort into our midst. The prayers in our (traditional) siddur do not suggest that God will bring redemption (ge'ulah), but a redeemer (go'eil). (The Reform movement has made the change to "ge'ulah.")
What kind of a world do we presume with these prayers? And what kind of attributes of God do we presume with these prayers? Neither question has a very uplifting answer, but that lesson is the first one about God – we do not get to choose God's will.