The variability of El Niño - La Niña events were analyzed in a low dimensional phase space - a concept derived from dynamic system theory. The space-time extended EOFs derived from diagnosing the space-time covariance matrix of the observed monthly mean SST field over tropical Pacific were used as the basis for the phase space to describe time evolution of the SST associated with El Niño - La Niña dynamics. It was shown that the basic features of the ENSO variability, such as the irregular oscillation, the phase-locking to the annual cycle and the inter-decadal changes in its propagation and onset, can be effectively represented by a 3-dimensional phase space. This provides and example of a complex system of the coupled ocean and atmosphere generating relatively simple dynamics in terns of a low dimensionality. The conclusion regarding the dimensionality of the ENSO system is derived from dynamic insights rather than through calculating the fractal dimensions. It is argued that the derivation of a fractal dimension is less plausible in many instances of physical realities, such as the ENSO dynamics. Besides, it is often more useful to know the minimum number of variables to describe the system than the fractal dimensions. Our conclusion regarding the dimensionality of the ENSO, derived from observational data, is consistent with those from dynamic model studies. The subsequent phase space analysis shows that the typical ENSO life cycle is about 4 years and that El Niño and La Niña are the opposite phase of the same dynamics, referred to as the ENSO signal. The observed biennial component may be a sub-harmonic of the 4-year life cycle. The role of annual cycle in the ENSO dynamics is most clearly demonstrated in the phase portraits. The inter-decadal variability is associated with the regime behavior and intermittency of the ENSO system, which is clearly revealed from the phase diagrams and the associated ENSO intensity.