The "end" value at a specified date in the future of an investment or cash flow.
Terminal value is a term used in value calculations looking forward toward the future value of an asset or cash flow, and also in calculations which start with the Terminal Value and depreciate the asset over the intervening years until one arrives at the Present Value.
Can be used in calculations regarding a business, an index, a cash flow, or an asset. Horizon Value is a synonym, and is perhaps better suited to describe the way the calculation chooses a time horizon of a specific number of years, but otherwise uses the same numbers in an equation that will estimate the value if the business or index went on growing at the same rate into perpetuity.
This is part of the nature of terminal/horizon value: the calculations project values into the future with as much accuracy as possible, but ultimately there are too many variables to control for, and any valuations far enough in the future should be stated as a range of probable outcomes.
The levered and un-levered assets are calculated at different discount rates. There are instances when terminal value is relatively certain: a bond at maturity, a piece of equipment at salvage value, a business at about book value (if it's going to be liquidated).