The UCLA site explains Cronbach's alpha as the average internal correlation among survey items. It also says that it is not a measure of unidimensionality. Rather, it is a measurement of internal consistency (though just intuitively I feel what is coherent tends to be also uni-dimensional... I think the point is that the measure is most optimal by design for the assessment of internal correlation, not dimentionality.
http://www.ats.ucla.edu/stat/spss/faq/alpha.html
Standardized versus Raw
This SAS website says one should use the standardized version of the measure (as opposed to raw).
It says: "Because the variances of some variables vary widely, you should use the standardized score to estimate reliability."
A note to myself: Does this mean if I standardized all items before the analysis, I get the same value for raw and standardized? I can experiment this.