Difference between strand-specific and not strand-specific RNA-seq data
It may be worth checking out the paper "Comprehensive comparative analysis of strand-specific RNA sequencing methods".

The most common techniques sequentially ligate different RNA adapters to the 5' and 3' ends of each RNA molecule prior to cDNA synthesis.  You will end up with an RNA molecule that looks like this (where A and B are the two adapters):

  5'-AAAAAA---------------BBBBBB-3'


These adapters are then used for cDNA synthesis and library preparation.  Finally, since each adapter is ligated to a specific end of the RNA the library can be generated in a stand-specific fashion; ie. the reads derived from the antisense strand should align to the antisense strand of the genome.

** Note that there are other variations of this technique but Illumina's protocol is one of the most popular.