i might not be right, but this is my take on why VaR is based on the 3 factors:
1. exposure - this is the amount at stake, given our tolerance (i.e. we do expect that this is the "maximum" amount that won't be exceeded given a tolerance level of 95%), over 10 days
2. volatility - the daily returns are quite volatile, and when considering a portfolio rather than an individual equity, the effects are "blanketed" (due to correlations, etc). therefore, VaR is our "best estimate" - a number that summarises up these volatilities.
3. liquidity - VaR is expressed for a given period of time. hence, given the "exposure" - it gives us an assessment of how much is required to reinstate our original position. it gives us an indicator of how much liquid assets need to be held in order to liquidate the "loss" in an orderly fashion (especially during adverse conditions).