Aims:We investigate the dynamics of the nebula around the symbiotic star Hen 2-147, determine its expansion parallax, and compare it with the distance obtained via the period-luminosity relation for its Mira variable. Methods: A combination of multi-epoch HST images and VLT integral field high-resolution spectroscopy is used to study the nebular dynamics both along the line of sight and in the plane of the sky. These observations allow us to build a 3D spatio-kinematical model of the nebula, which, together with the measurement of its apparent expansion in the plane of the sky over a period of 3 years, provides the expansion parallax for the nebula. Additionally, SAAO near-infrared photometry obtained over 25 years is used to determine the Mira pulsation period and derive an independent distance estimation via the period-luminosity relationship for Mira variables. Results: The geometry of the nebula is found to be that of a knotty annulus of ionized gas inclined to the plane of sky and expanding with a velocity of ~90 km s-1. A straightforward application of the expansion parallax method provides a distance of 1.5 ± 0.4 kpc, which is a factor of two lower than the distance of 3.0 ± 0.4 kpc obtained from the period-luminosity relationship for the Mira (which has a pulsation period of 373 days). The discrepancy is removed if, instead of expanding matter, we are observing the expansion of a shock front in the plane of the sky. This shock interpretation is further supported by the broadening of the nebular emission lines. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract No. NAS5-26555; on observations obtained at the 8 m VLT telescope of the European Southern Observatory in Chile; and on observations made at the South African Astronomical Observatory. The movie (Fig. 3) is only available in electronic form at http://www.aanda.org Table 2 is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/465/481