Underwater wireless optical communication (UWOC) has been widely studied as a key technology for ocean exploration and exploitation. However, current UWOC systems neglect semantic information of transmitted symbols, leading to unnecessary consumption of communication resources for transmitting non-essential data. In this paper, we propose and demonstrate a deep-learning-based underwater wireless optical semantic communication (UWOSC) system for image transmission. By utilizing a deep residual convolutional neural network, the semantic information can be extracted and mapped into the transmitted symbols. Moreover, we design a channel model based on long short-term memory network and employ a two-phase training strategy to ensure that the system matches the underwater channel. To evaluate the performance of the proposed UWOSC system, we conduct a series of experiments on an emulated UWOC experimental platform, in which the effects of different turbidity channel environments and bandwidth compression ratios are investigated. Experimental results show that the UWOSC system exhibits superior performance compared to the conventional communication schemes, particularly in challenging channel environments and low bandwidth compression ratios.