Propaganda plays a critical role in shaping public opinion and fueling disinformation. While existing research primarily focuses on identifying propaganda techniques, it lacks the ability to capture the broader motives and the impacts of such content. To address these challenges, we introduce propainsight, a conceptual framework grounded in foundational social science research, which systematically dissects propaganda into techniques, arousal appeals, and underlying intent. propainsight offers a more granular understanding of how propaganda operates across different contexts. Additionally, we present propagaze, a novel dataset that combines human-annotated data with high-quality synthetic data generated through a meticulously designed pipeline. Our experiments show that off-the-shelf LLMs struggle with propaganda analysis, but training with propagaze significantly improves performance. Fine-tuned Llama-7B-Chat achieves 203.4% higher text span IoU in technique identification and 66.2% higher BertScore in appeal analysis compared to 1-shot GPT-4-Turbo. Moreover, propagaze complements limited human-annotated data in data-sparse and cross-domain scenarios, showing its potential for comprehensive and generalizable propaganda analysis.