The noun “breadth” is another word for width, or the distance from side to side of something. The speaker suggests that love, which is generally considered to be an abstract concept, is a measurable entity that fills the space that her soul can reach.
While “end” is commonly read as the point at which something stops, it can also refer to something’s function or purpose. Here, it’s possible that Browning’s speaker is using it that way to describe a feeling of purposelessness.
