Different biological samples, for example if you are studying the expression for the leaf development at three different stages (young, mature and senesce leaf), three different biological replicates will be three different pools of 2-5 leaves of at least 3 different plants (5 is convenient, > 20 is great). The goal of a biological replicate is to capture the biological variability in the experimental sample. In other words, if you are comparing young and mature leaves, you want to see differences between these two stages, not the differences between these two stages + two individuals. If you take biological sample replicate (same leaves pool), and you do two different libraries, you will have two technical replicates (not biological).
Please take a look to the this page from UCDavis (http://wiki.bioinformatics.ucdavis.edu/index.php/RNAseq_experimental_design) for a more complete explanation.
A Biological replicate always means an independent biological sample treated under the same conditions. In case of RNA seq it would be RNA purified from an independent batch of cells. Sequencing the same sample twice or from independent libraries prepared form the same biological sample constitutes technical replicates.
As Swaminathan said, If you are sequencing the same RNA extraction twice means that you are doing technical replicates. In order to get a biological replicate you will need to use the RNA from different bach of cells or or organism treated at the same condition