A flare from the TeV blazar Mrk 421, occurring in March 2010, was observed for 13 consecutive days from radio to very high energy (VHE; E>100GeV) gamma-rays with MAGIC, VERITAS, Whipple, FermiLAT, MAXI, RXTE, Swift, GASP-WEBT, and several optical and radio telescopes. We model the day-scale SEDs with one-zone and two-zone synchrotron self-Compton (SSC) models, investigate the physical parameters, and evaluate whether the observed broadband SED variability can be associated to variations in the relativistic particle population. Flux variability was remarkable in the X-ray and VHE bands while it was minor or not significant in the other bands. The one-zone SSC model can describe reasonably well the SED of each day for the 13 consecutive days. This flaring activity is also very well described by a two-zone SSC model, where one zone is responsible for the quiescent emission while the other smaller zone, which is spatially separated from the first one, contributes to the daily-variable emission occurring in X-rays and VHE gamma-rays. Both the one-zone SSC and the two-zone SSC models can describe the daily SEDs via the variation of only four or five model parameters, under the hypothesis that the variability is associated mostly to the underlying particle population. This shows that the particle acceleration and cooling mechanism producing the radiating particles could be the main one responsible for the broadband SED variations during the flaring episodes in blazars. The two-zone SSC model provides a better agreement to the observed SED at the narrow peaks of the low- and high-energy bumps during the highest activity, although the reported one-zone SSC model could be further improved by the variation of the parameters related to the emitting region itself ({delta}, B and R), in addition to the parameters related to the particle population.