Ergodic means meandering all over.
In the jumping particle example given by Davies, (The Cosmic Blueprint, p. 33) if we look at any interval on the line, it will be visited over and over again by the particle, no matter how small the region of interest, wherever it is. There are no gaps. The result of the sufficient repetition of certain effects of chance thus produces forms of regularity.
In a phase space, volumes of low probability are small, while volumes of high probability are large. If the system wanders about ergodically, the relative sizes of the volumes are a direct measure of their probability. Thus, for Boltzman, the increase in entropy in equilibrium systems arises from nothing more than the statistical tendency of the system to pass randomly through all possible arrangements. This is the so-called ergodic hypothesis -- that the system's trajectory will wander aimlessly, or ergodically, in phase space.
Because of this wandering of the system, the maintenance of order requires work.
If we think of the intial state of a system as a bundle of nearby points rather than a single point, this small volume in the state space can be thought of as a microstate. Vastly many microstates of the system are in the equilibrium macrostate. In a simple system, the bundle retains its shape and moves in a regular manner over a restricted region of the state space. In an ergodic system, it retains its shape but now moves all over the state space. In a chaotic system, it loses its shape and spreads out like a drop of ink in water, eventually invading every part of the space. the ensemble of states fills the available phase space. Like a fractal, any state of the system continues to divide over time. An ergodic system may also have an attractor whose form remains the same but whose size is unlimited and can cover all of phase space (see Prigogine and Stengers p. 266)
According to Stuart Kauffman, the universe is massively non-ergodic, particularly the biosphere. The time it would take to make all possible proteins of length 200, for example, is some 10 to the 67th times the age of the universe. Thus it is impossible for all possible proteins to be synthesized at least once. For Kauffman, "The nonergodicity of the universe as a whole and the biosphere in particular is interesting from another point of view. History enters when the space of the possible that might have been explored is larger, or vastly larger, than what has actually occurred." (Investigations, p.152)
See J. Lebowitz and O. Penrose, "Modern Ergodic Theory", Physics Today (Feb 1973) pp. 23-29.