The parasitic elements act as resonators and couple electromagnetically with the driven element, and serve to modify the radiation pattern of the antenna, directing the radio waves in one direction, increasing the gain of the antenna.
A log-periodic antenna (LPDA) consists of many dipole elements of decreasing length, all of which are driven.
Household multiband television antennas generally consist of a hybrid between a UHF Yagi with one driven dipole and a log-periodic for VHF behind that with alternating active elements.
The driven elements between the UHF and VHF are then coupled and often matched for a 75 Ω coaxial downlead to the receiver.
The driven element of the antenna is usually a half-wave dipole, its length half a wavelength of the radio waves used.
Although sometimes the parasitic elements are insulated from the supporting beam, often they are clamped or welded directly to it, electrically connected to it.
This doesn't affect their functioning, because the RF voltage distribution along the element is maximum at the ends and goes to zero (has a node) at the midpoint where the grounded beam is attached.
The addition of parasitic elements gives a diminishing improvement in the antenna's gain.