。
She wanted me to come.
Literal
She [topic-は] me [to-に] come-receive want-to [showing-がる-was-progressive-ていた].
Three layered grammar pieces compress into one verb chain: 来てもらう (have someone come, benefactive 'I receive their coming'), then ~たい (want to do), then ~たがる (a third-person desire marker — 'shows signs of wanting,' since you can't directly assert another person's feeling). On top of that, the past progressive ~ていた marks an ongoing state in the past. The whole stack captures a subtle nuance English flattens: she wanted me to come, and was visibly displaying that desire over time. The grammar respects the boundary that you don't claim to know another person's interior feeling, only its outward signs.