We present a pan-chromatic analysis of an unprecedented sample of 1402 250 micron-selected galaxies at z < 0.5 (mean z = 0.24) from the Herschel-ATLAS survey. We complement our Herschel 100-500 micron data with UV-K-band photometry from the Galaxy And Mass Assembly (GAMA) survey and apply the MAGPHYS energy-balance technique to produce pan-chromatic SEDs for a representative sample of 250 micron selected galaxies spanning the most recent 5 Gyr of cosmic history. We derive estimates of physical parameters, including star formation rates, stellar masses, dust masses and infrared luminosities. The typical H-ATLAS galaxy at z < 0.5 has a far-infrared luminosity in the range 10^10 - 10^12 Lsolar (SFR: 1-50 Msolar/yr) thus is broadly representative of normal star forming galaxies over this redshift range. We show that 250 micron-selected galaxies contain a larger mass of dust at a given infra-red luminosity or star formation rate than previous samples selected at 60 micron from IRAS. We derive typical SEDs for H-ATLAS galaxies, and show that the emergent SED shape is most sensitive to specific star formation rate. The optical-UV SEDs also become more reddened due to dust at higher redshifts. Our template SEDs are significantly cooler than existing infra-red templates. They may therefore be most appropriate for inferring total IR luminosities from moderate redshift submillimetre selected samples and for inclusion in models of the lower redshift submillimetre galaxy populations.