This paper presents an improved understanding of the dynamic focusing process and lateral migration dynamics of microparticles throughout a classic spiral microchannel at finite Reynolds numbers. A novel two-stage model is proposed to elucidate the particle focusing process along the channel. Specifically, we find that particle migration undergoes a two-stage development comprising the formation of the particle array (stage I) and the shifting of the focusing position after particles are well focused (stage II). Variations in particle focusing ratio and lateral focusing position under different migration lengths and different driving flow rates are quantitatively investigated and analyzed. Results show that the cross-sectional Dean flow affects the particle migration dynamics throughout the channel more significantly at large Reynolds numbers. It is also found that an unstable focusing phenomenon occurs at the intermediate channel region in addition to at the outlets. A state diagram is then generated to illustrate the occurrence and development of this interesting focusing instability along the channel. In addition, the focusing performances of a mixture of different size particles are investigated to reveal the multi-particle separation process and mechanism. The small particle is found to contribute more significantly to the variation in the relative positions of multi-particles. These improved understandings of the particle focusing mechanisms provide insights into the device optimization and the operation protocol improvement.