A parfocal lens is a lens that stays in focus when magnification/focal length is changed. There is inevitably some amount of focus error, but small enough to be considered insignificant.
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Microscopy
Parfocal microscope objectives stay in focus when magnification is changed; i.e., if the microscope is switched from a higher power objective (e.g., 40×) to a lower power objective (e.g., 10×), the object stays in focus. Ideally, most bright-field microscopes are parfocal.
Photography
Zoom lenses (sometimes referred to as "true" zoom) are ideally parfocal in that focus is maintained as the lens is zoomed (focal length and magnification changed), which not only is convenient, but also has the advantage of allowing more accurate focusing at maximal focal length and then zooming back to a shorter focal length to compose the image.
Many zoom lenses, particularly in the case of fixed-lens cameras, are actually varifocal lenses, which gives lens designers more flexibility in optical design trade-offs (focal length range, maximal aperture, size, weight, cost) than parfocal zoom, and which is practical because of auto-focus, and because the camera processor can automatically adjust the lens to keep it in focus while changing focal length ("zooming"), making operation practically indistinguishable from a parfocal zoom.
Cinematography
Zoom lenses used for moviemaking applications must have the parfocal ability in order to be of practical use. It is almost impossible to stay in correct focus (as done manually by the focus puller) while zooming. This could be possible theoretically, but if the subject and/or camera also move, there are too many variables to correct consistently.
Telescopes
Parfocal telescope eyepieces stay in focus when magnification is changed; i.e., if the telescope is switched from a lower-power eyepiece (e.g., 10×) to a higher-power eyepiece (e.g., 20×), or vice versa, the object stays in focus.