。
She choked on a piece of bread.
Literal
She [topic-は] bread [object-を] throat [in-に] caused-to-clog.
詰まらせる is the causative form of 詰まる ('to be clogged, blocked, stuck') — the underlying intransitive describes something getting stuck, while the causative says she 'caused [the bread] to get stuck' in her throat. Causatives of intransitives often render in English as accidental causation: '[she] choked on the bread.' に here marks the location where the choking happened — at the throat. パン is a Portuguese loanword from pão, brought to Japan by 16th-century Portuguese missionaries along with Catholic communion bread; the word stayed even after Christianity was suppressed, and Japan's pastry-and-bread culture grew up around this Portuguese-derived word.