The yield curve is the relation between the interest rate and the time to maturity of the debt for a given borrower in a given currency.
The expectation theory assumes that the various maturities are perfect substitutes and suggests that the shape of the yield curve depends on market participants' expectations of future interest rates. These expected rates, along with an assumption that arbitrage opportunities will be minimal, is enough information to construct a complete yield curve.
For example, if investors have an expectation of what 1-year interest rates will be next year, the 2-year interest rate can be calculated as the compounding of this year's interest rate by next year's interest rate.
This theory perfectly explains the stylized fact that yields tend to move together. However, it fails to explain the persistence in the shape of the yield curve.