Where can I find accessible reference to vector autoregression? I would like to understand the topic conceptually rather than through equations
 A: maybe here (free but add supported(sic)), chapter 6.
Best to develop intuition is to try with a software package 
that does not require too much overhead
A: Vector autoregression is the same as autoregression, but using a vector of time series, rather than a single time series...which makes the 'vector' effectively a matrix. Economists call the combination of cross-sectional and longitudinal data 'panel data'. Although googling that gets esoteric pretty quickly. 
I find it easier to think of as an iterative process: With each new time period, the new value in each depends on a) the coefficients of the previous equation for the time series, and b) the coefficients of the previous values of all the other time-series in the dataset. 
previous value in the series, and b) the previous values of the one data point, and b) the previous values of all the other the coefficients of the previous OLS regression line c) the coefficients of the previous regression line
"VAR models (vector autoregressive models) are used for multivariate time series. The structure is that each variable is a linear function of past lags of itself and past lags of the other variables"
Vector autoregression (VAR) is an econometric model used to capture the linear interdependencies among multiple time series. VAR models generalize the univariate autoregression (AR) models by allowing for more than one evolving variable. All variables in a VAR are treated symmetrically in a structural sense...each variable has an equation explaining its evolution based on its own lags and the lags of the other model variables. 
A: You can not understand anything in statistics without equations. You may fool yourself into thinking that you understand something conceptually, but this kind of understanding will be utterly useless.
There are many texts on vector autoregression (VAR) models. I think these lecture notes are quite simple. Yes, it has equations, but it also has very simple S-PLUS code to play with. S-PLUS is very similar to R, you should be able to run the code snippets in R too.
