In a mutually coupled antenna array (notably a Yagi-Uda antenna), the driven element is the single antenna that has an applied source feed. The other antenna elements are not excited (or driven). There are a few resons why one would only drive one element of the array. Doing this in the manner of a Yagi-Uda array allows for the field patterns to be directed in one direction with increased gain. The other elements are parasitic and take advantage of mutual coupling to aim the antenna. In a log periodic dipole array (LPDA), only one of the many dipoles is driven at a time. The dipole that is driven depends on the frequency of the signal. The advantage of this over an antenna such as a Yagi, which is only designed for one frequency, is that the antenna can be made relatively broadboand (nearly 2:1) by exciting differently sized elements that are resonant at different frequencies.
Note that when a "driven element" is referred to in an antenna array, it is assumed that other elements are not driven (i.e. parasitic) and that the array is tightly coupled (spacing far below a wavelength). It is also possible to have multile driven elements in an array. For example, a two element array spaced a quarter wavelength apart has a distinct cardioid pattern when the second element is driven with a source -90 degrees out of phase relative to the source of the first element.