Fanning your seam allowances means spreading out the fabric in those spots where several seams come together to evenly distribute the bulk and avoid bumps.
Here is an example of how to fan seam allowances on a four-patch block. All four pieces have been sewn together, and the block is ready for pressing. Click on images for a larger view.
Unpick the last part of the seam until you come to the cross seam (see arrow). Unpick this part on the back side as well
Open the block, and you can see how the seam allowances are already going counter-clockwise even before pressing (see arrows).
Press block carefully from the left side, and you are done. This is a simple trick to avoid bumps without having to press seams open.