Recently, there has been a growing trend in utilizing large language models (LLMs) for recommender systems, referred to as LLMRec. A notable approach within this trend is not to fine-tune these models directly but instead to leverage In-Context Learning (ICL) methods tailored for LLMRec, denoted as LLM-ICL Rec. Many contemporary techniques focus on harnessing ICL content to enhance LLMRec performance. However, optimizing LLMRec with ICL content presents unresolved challenges. Specifically, two key issues stand out: (1) the limited understanding of why using a few demonstrations without model fine-tuning can lead to better performance compared to zero-shot recommendations. (2) the lack of evaluation metrics for demonstrations in LLM-ICL Rec and the absence of the theoretical analysis and practical design for optimizing the generation of ICL content for recommendation contexts. To address these two main issues, we propose a theoretical model, the LLM-ICL Recommendation Equivalent Gradient Descent model (LRGD) in this paper, which connects recommendation generation with gradient descent dynamics. We demonstrate that the ICL inference process in LLM aligns with the training procedure of its dual model, producing token predictions equivalent to the dual model's testing outputs. Building on these theoretical insights, we propose an evaluation metric for assessing demonstration quality. We integrate perturbations and regularizations in LRGD to enhance the robustness of the recommender system. To further improve demonstration effectiveness, prevent performance collapse, and ensure long-term adaptability, we also propose a two-stage optimization process in practice. Extensive experiments and detailed analysis on three Amazon datasets validate the theoretical equivalence and support the effectiveness of our theoretical analysis and practical module design.