The phrase doesn't relate to actual magic; it's about impressing with skill or expertise. Everyone was struggling with the bug, but when Lisa came, she managed to weave her magic.
Pro Tip 2/3
Positive Connotations
Using 'weave your magic' usually suggests a positive outcome or an impressive accomplishment. The team was behind, but the coach wove his magic with a motivational speech.
Pro Tip 3/3
Subjective Impact
What's considered 'magic' may differ among people, depending on what impresses them. To the children, the clown wove his magic simply by making balloon animals.