The thunder frightened the students.

Literal

Thunder [topic-は] students [object-を] frighten-caused.

怖がらせる is the causative of 怖がる — '[X] makes [Y] frightened.' Built as 怖がる → 怖がらせる. Causatives mark the agent of fear with を (or に in some contexts). Causative + ~がる stacks two grammatical operations: 'cause to show fear.'