Woven cloth is composed of threads on two axes. Let's call them N/S and E/W. (Technically, they are warp and weft.) If you pull the N/S threads or the E/W threads, there is very little give in the fabric because you're pulling directly on the structure of the fabric.
Bias exploits the weakness of the spaces between the threads. If you pull the NW and SE corners of the fabric - the red arrow - the little square spaces between the threads deform into little parallelogram spaces. (The same applies for the NE/SW bias axis.)
The gray fabric above is a straight strip that has been deformed to lie smoothly along a curved neckline. While a bias strip can be deformed with just the fingers, a little coaxing with a steam iron assures a very smooth curve.
Bias strips can be deformed on both inside and outside curves. In the example below there was a lot of questionable language as I repeatedly steamed my fingers.
Bias tape or binding is available commercially, but only in solid colors, and typically only in a cotton-polyester blend, so I almost always cut my own. I'll cut more than I need for the project at hand, so over time I've developed a nice back stock of bias strips. In many sewing projects, the bias strip isn't visible from the outside of the garment, and it gives me great joy to use several different prints in a single garment.
The edge-stitching in the black example a little wobbly - I'm between cataract surgeries, so I can only really see close work out of one eye.
*I've borrowed liberally from "Beer is proof that God loves us and wants us to be happy," which is wrongly attributed to Benjamin Franklin.
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