I love Dane Ortlund’s succinct definition

By ‘inaugurated eschatology’ I mean the launching in the middle of history of that which the OT promised would happen at the end of history. The last things (eschatology) have already begun (inaugurated). NT eschatology is not about the future but about the inbreaking of the future into the present, through Christ.

He has a couple more quotes on inaugurated eschatology on his blog.