Thanks Sahil for your feedback! Your question is not at all silly.

Suppose the time series under consideration is the stock price of Google.

y_t = stock price at time t.

Once the markets have closed, y_t is constant for all t until they reopen. So it’s variance is zero and so there is no variance to 'explain’.

However during the day, y_t moves up and down around some expected value, and so y_t has a variance > 0 that some other factors can influence (a.k.a. explain).

Suppose someone tells you that the previous time period’s stock price can be used to predict the current time period’s price in a linear manner. So your model for y_t would be:

y_t = beta_0 + beta_1*y_(t-1) + epsilon

Where epsilon is the unexplained error, i.e. the fraction of the variance in y_t which changes in y_(t-1) couldn’t explain.

Say another friend tells you that y_(t-2) also influences y_t independent of y_(t-1). Now your model becomes:

y_t = beta_0 + beta_1*y_(t-1) + beta_2*y_(t-2) + epsilon_2

Where epsilon_2 < epsilon, i.e. the unexplained variance in y_t has now (presumably) reduced.

Now bear in mind that the reason y_(t-1) and y_(t-2) are able to explain any variance in y_t at all, is because they themselves are not constant, i.e. the explanatory variables too have a variance of their own around their individual expected values.

Hence what we are really saying is that the variance in y_(t-1) is explaining some of the observed variance in y_t via the coefficient beta_1. And whatever variance in y_t is left over, some of that remaining balance is explained by the variance in y_(t-2) via the coefficient beta_2.

The remaining amount of unexplained variance in y_t is collected as residue in the residual errors epsilon_2.

I hope this helps.

'best