I'm so confused about what aranea did to jake. On the wiki it says she "restored his mind" like she did with Terezi's sight. Was he crazy? Or had he lost hope? I'm confused. I thought she just like somehow gave him so much hope it triggered his hope powers

It’s hard to tell exactly what she DID do to him- Restoring his Mind or Restoring his Hope makes no Sense, because she is a Sylph of LIGHT, not Hope or Mind! You could associate Light with ‘seeing the Light’, ‘being Enlightened’ and other things that she could’ve done to him, but what I think fits the experience better? She made him a beacon of Relevancy. She empowered him through Light to become the most Important event in the entire Session- Which in that case manifested as her unlocking his Page of Hope Potential, even if temporarily.