We present very-high-energy gamma-ray observations of the BL Lac object 1ES 2344+514 taken by the Very Energetic Radiation Imaging Telescope Array System between 2007 and 2015. 1ES 2344+514 is detected with a statistical significance above the background of 20.8 sigma in 47.2 h (livetime) of observations, making this the most comprehensive very-high-energy study of 1ES 2344+514 to date. Using these observations, the temporal properties of 1ES 2344+514 are studied on short and long times-scales. We fit a constant-flux model to nightly and seasonally binned light curves and apply a fractional variability test to determine the stability of the source on different time-scales. We reject the constant-flux model for the 2007-2008 and 2014-2015 nightly binned light curves and for the long-term seasonally binned light curve at the > 3 sigma level. The spectra of the time-averaged emission before and after correction for attenuation by the extragalactic background light are obtained. The observed time-averaged spectrum above 200 GeV is satisfactorily fitted (x(2)/NDF = 7.89/6) by a power-law function with an index Gamma = 2.46 +/- 0.06(stat) +/- 0.20(sys) and extends to at least 8 TeV. The extragalactic-backgroundlight-deabsorbed spectrum is adequately fit (x(2)/NDF = 6.73/6) by a power-law function with an index Gamma = 2.15 +/- 0.06(stat) +/- 0.20(sys) while an F-test indicates that the power law with an exponential cut-off function provides a marginally better fit (x(2)/NDF = 2.56/5) at the 2.1 sigma level. The source location is found to be consistent with the published radio location and its spatial extent is consistent with a point source.