A Herschelian telescope is an off-axis reflector telescope with one mirror: a primary mirror that reflects toward one side. The type is named for William Herschel who (among other things) created very large telescopes for his day using such a design, the largest with a 1.2m aperture.
I would guess the primary mirror might be spherical for ease in manufacture but I've seen Herschel's described as parabolic. Either will cause geometrical aberrations, which Herschel limited by using a long focal length. The mirrors of the day had low reflectivity, a motivation for avoiding additional mirrors.
Such off-axis telescopes (and equivalent antenna reflectors) have now become common, e.g., for radio telescopes, now that computers help create and validate the designs, but in many cases, they incorporate additional mirrors/reflectors.