She got close to them at the school festival.

Literal

She [topic-は] school-festival [at-で] them [with-と] close became.

学園祭 is the school-wide festival held at universities and some high schools, distinct from 文化祭 (typically a cultural-arts-focused festival at high schools). Both feature student-run booths (出店), performances (ステージ), and themed displays (展示) — events where students plan, build, and run everything themselves over the course of a weekend. They're a major social moment in school life, where shared work and chaotic excitement push together students who might never otherwise interact. 親しくなる ('to become close / friendly') uses the i-adjective 親しい ('intimate, close') in adverbial form 親しく + なる ('become') — the standard adjective-to-state-change pattern. と marks the people one became close with.