A possible mechanism of the appearance of turbulent structures in plasma is considered as a result of the development of unstable ion temperature gradient (ITG) drift waves, both with and without a sheared flow. A description of several stages of the drift wave evolution is proposed. The condition for limiting the growth of the wave amplitude is discussed. A qualitative agreement of the results with the theoretical and experimental results of other authors is shown. The motion of particles in the wave and vortex structures is studied on the basis of the proposed mechanism and ideas of other authors.