The wide spread of location-based social networks brings about a huge volume of user check-in data, which facilitates the recommendation of points of interest (POIs). Recent advances on distributed representation shed light on learning low dimensional dense vectors to alleviate the data sparsity problem. Current studies on representation learning for POI recommendation embed both users and POIs in a common latent space, and users' preference is inferred based on the distance/similarity between a user and a POI. Such an approach is not in accordance with the semantics of users and POIs as they are inherently different objects. In this paper, we present a novel spatiotemporal aware (STA) representation, which models the spatial and temporal information as \emph{a relationship connecting users and POIs}. Our model generalizes the recent advances in knowledge graph embedding. The basic idea is that the embedding of a $<$time, location$>$ pair corresponds to a translation from embeddings of users to POIs. Since the POI embedding should be close to the user embedding plus the relationship vector, the recommendation can be performed by selecting the top-\emph{k} POIs similar to the translated POI, which are all of the same type of objects. We conduct extensive experiments on two real-world datasets. The results demonstrate that our STA model achieves the state-of-the-art performance in terms of high recommendation accuracy, robustness to data sparsity and effectiveness in handling cold start problem.