From Janet Wickell,
Your Guide to Quilting.
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There are no threads to stabilize fabric along the bias, so cuts with their edges along the bias are quite stretchy. The stretch can work for you or against you:

Helpful Bias Edges

• Long, stretchy strips cut along the bias are easy to apply as binding to a quilt with curved edges.

• Thin tubes made from bias cut strips can be shaped to form stems and other delicate shapes for applique.

• Bias cuts can be turned under easier for some curved and slanted applique shapes, like hearts.

Problem Bias Edges

• Bias edges placed along the outer edges of quilt blocks or other components can stretch out of shape as you handle the quilt during construction, making it difficult to match and sew pieces together accurately.

• Triangles always have at least one bias edge. Analyze the pattern to determine the best placement for it--usually on a block's interior and sewn to a straight grain piece when possible for stabilization.

There will be times when you decide to cut a patch with bias edges in the "wrong" position in order to use a specific part of a print or to make it flow with its neighbors. Occasional wayward patches are fine--just pay attention to where the stretchy bias edges are and handle them with care.