Father [subject-が] war's experience-stories [object-を] told-for-me.
体験談 = 'personal account of experiences' — 体験 (experience) + 談 (talk/story). 語ってくれた uses 語る ('to narrate/tell,' more literary than 話す) with てくれた (did for me as a favor). A poignant image of intergenerational storytelling.