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We present an observational study using high-resolution echelle spectroscopy of collisionless shocks in the Cygnus Loop supernova remnant. Measured Hα line profiles constrain pre-shock heating processes, shock speeds, and electron-ion equilibration (T_e/T_i). The shocks produce faint Hα emission line profiles, which are characterized by narrow and broad components. The narrow component is representative of the pre-shock conditions, while the broad component is produced after charge transfer between neutrals entering the shock and protons in the post-shock gas, thus reflecting the properties of the post-shock gas. We observe a diffuse Hα region extending about 2.'5 ahead of the shock with line width ∼29 km/s, while the Hα profile of the shock itself consists of broader than expected narrow (36 km/s) and broad (250 km/s) components. The observed diffuse emission arises in a photoionization precursor heated to about 18,000 K by He I and He II emission from the shock, with additional narrow component broadening originating from a thin cosmic-ray precursor. Broad to narrow component intensity ratios of ∼1.0 imply full electron-ion temperature equilibration T_e≃ T_i in the post-shock region. Broad component line widths indicate shock velocities of about 400 km/s. Combining the shock velocities with proper motions suggests that the distance to the Cygnus Loop is ∼890 pc, significantly greater than the generally accepted upper limit of 637 pc.