If we consider the two largest masses in our solar system - the Sun and Jupiter, by themselves, they will orbit a common barycenter which is somewhere offset from the Sun's center in the direction of Jupiter (just above the Sun's surface). If we add Saturn, things get more complicated, but there is still a barycenter, even if it follows a complex path with respect to the Sun's center (or the Sun has a complex wobble around the barycenter). Add Neptune and all the other masses in the solar system, and things get even more complicated. Neverthess, there is still a barycenter (often outside the limb of the Sun) about which the Sun does a complex dance.
Now, what is Earth actually orbiting? The Earth's orbit is described to be an ellipse; the "center" of an elliptical orbit occurs at one of the focal points of the ellipse. What is at the focal point of the elliptical path the Earth follows? Is it the solar system barycenter or is it the Sun's (wobbling) center of mass? In other words, is the Earth's orbit shifting as the Sun is tugged around, our distance from the Sun never varying by more than the eccentricity of the ellipse, or do we orbit the solar system barycenter, and our distance from the Sun varies by the sum of our orbital eccentricity plus the amount the Sun wobbles in its own orbit around the barycenter?