In Christian theology, doctrines of the "last things". Eschatology is a relatively young field in systematic theology, having only been recognized as such since the 18th century.
Eschatology is divided roughly into two categories: personal and cosmic.
Personal Eschatology pertains to the last things wrt a particular individual, and speaks to matters such as:
Cosmic Eschatology asks the questions that make for New York Times Bestsellers.
What will the great tribulation be like? Will there be one per se? How long will it last? (Conventional wisom: seven years)
What about the rapture?
What is the meaning of the Millennium in The Revelation of St. John?
What is the nature and essence of the Kingdom of God as it will be revealed in the eschaton?
What is the nature of that Kingdom as it relates to the People of God awaiting its consumation?
Ultimately, an eschatology is fundamentally important to the application of the rest of a theological system to the real world. It tells you whether things are getting better or the world is going to hell in a handbasket, what part the church is expected to play (or not play) in this, and even what the encounter of day-to-day Christian life should be like.
For example, if one accepts dispensational premillennialism, then one naturally expects widespread apostacy in the church, rejection of the gospel, and general ineffectiveness of Christ-centered ministry. If one accepts Gordon Fee's interpretation of the role of the Holy Spirit as the (at least partial) realization of the eschatological Kingdom, then one expects the supernatural to be commonplace in the church.