The intercept has a meaning here, as in any regression. But the meaning is neither interesting nor useful.
As calendar year is the predictor, the intercept here is the value predicted for year 0.
Set aside the fact that there was no year 0 and years are reckoned in retrospect, in the calendar you are using, to have run ..., 1 BC (or BCE), 1 (AD), etc. See on that http://en.wikipedia.org/wiki/0_(year) if curious.
The larger fact is that year 0 is way outside your data. Depending on what you are measuring, your response variable may not even have been defined 2000 or so years ago, as if for example it is some business or economic measure.
You would get a more interesting intercept if you used as predictor (year $-$ 2000), say. Then your intercept would be the value predicted when (year $-$ 2000) = 0, or more plainly year is 2000. A pleasant side-effect would be that its confidence interval would be narrower than that you report. Another pleasant side-effect would be that you could see for itself on a graph that the intercept was a sensible value. (Your difficulty would be plainer to you if you plot your data and think about what happens when you project the fitted line to year 0.)
The slope is naturally unaffected by a shift in origin.
Using a nice round number for origin is not the only choice. There are arguments for centring regressions on the means of all variables.
This problem is in no sense intrinsic to time series, and could arise with any data where a value of 0 for the predictor is way outside the range of the data and extrapolations to it are neither interesting nor useful. A regression of weight on height for adults would yield an intercept that was the weight predicted for a person of zero height, for example.
Similarly, this is not a SPSS problem, as similar results presumably would be obtained in any other software.
EDIT: See also related discussion in my answer is How to get exponential regression equation after performing linear regression on the log transformed equation?
EDIT 2: This paper discusses the question of species of origin more broadly.