To delete any object (handwriting, text, shapes, images, or highlights) you can first select what you wish to delete. Then tap Delete (trashcan icon). You can delete multiple objects at once by using the lasso method to select more than one object before tapping Delete.
In addition, you can delete handwriting, shapes, and highlights using the stroke eraser tool. The stroke eraser (the first of the two erasers in the tool picker) allows you to delete entire stroke based objects by simply tapping or swiping over them.