We present low-resolution 5.5-35 mum spectra for 103 galaxies from the 12 mum Seyfert sample, a complete unbiased 12 mum flux limited sample of local Seyfert galaxies selected from the IRAS Faint Source Catalog, obtained with the Infrared Spectrograph (IRS) on-board Spitzer Space Telescope. For 70 of the sources observed in the IRS mapping mode, uniformly extracted nuclear spectra are presented for the first time. We performed an analysis of the continuum emission, the strength of the polycyclic aromatic hydrocarbon (PAH) and astronomical silicate features of the sources. We find that on average, the 15-30 mum slope of the continuum is langalpha_15-30rang = -0.85 ± 0.61 for Seyfert 1s and -1.53 ± 0.84 for Seyfert 2s, and there is substantial scatter in each type. Moreover, nearly 32% of the Seyfert 1s, and 9% of the Seyfert 2s, display a peak in the mid-infrared spectrum at 20 mum, which is attributed to an additional hot dust component. The PAH equivalent width decreases with increasing dust temperature, as indicated by the global infrared color of the host galaxies. However, no statistical difference in PAH equivalent width is detected between the two Seyfert types, 1 and 2, of the same bolometric luminosity. The silicate features at 9.7 and 18 mum in Seyfert 1 galaxies are rather weak, while Seyfert 2s are more likely to display strong silicate absorption. Those Seyfert 2s with the highest silicate absorption also have high infrared luminosity and high absorption (hydrogen column density N_H > 10²³ cm^-2) as measured from the X-rays. Finally, we propose a new method to estimate the active galactic nucleus contribution to the integrated 12 mum galaxy emission, by subtracting the "star formation" component in the Seyfert galaxies, making use of the tight correlation between PAH 11.2 mum luminosity and 12 mum luminosity for star-forming galaxies.