Thomas precession is a consequence of Wigner rotation, which arises because there is no group of three-dimensional Lorentz boosts: two noncollinear boosts generally compose to a boost plus
a rotation, and the latter cannot be eliminated. This is in contrast with the group of Galilean transformations, in which there is a three-dimensional group of Galilean boosts: two successive Galilean boosts compose to another pure Galilean boost.
In the Lorentz case, the coordinate axes of a rigid body undergoing relativistic circular motion under the action of a torque-free force precess in the opposite sense to the circular motion through an angle of
for each circuit of the motion, where
is the Lorentz factor. This angle is negative, showing the sense of precession counter to
the sense of circular motion.
In contrast, in Newtonian torque-free circular motion (i.e., with the net force directed toward the center of the circle through the center of mass), the body's axes maintain a constant direction. Reference  presents a simple, intuitive derivation of this phenomenon.
 C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation
, San Francisco: W. H. Freeman, 1973 Section 6.6.
 A. Dragan and T. Odrzygóźdź, "A Half-Page Derivation of the Thomas Precession," American Journal of Physics
, 2013 p. 631–632. doi:10.1119/1.4807564