Online news domains increasingly rely on social media to drive traffic to their websites. Yet we know surprisingly little about how a social media conversation mentioning an online article actually generates clicks. Sharing behaviors, in contrast, have been fully or partially available and scrutinized over the years. While this has led to multiple assumptions on the diffusion of information, each assumption was designed or validated while ignoring actual clicks. We present a large scale, unbiased study of social clicks - that is also the first data of its kind - gathering a month of web visits to online resources that are located in 5 leading news domains and that are mentioned in the third largest social media by web referral (Twitter). Our dataset amounts to 2.8 million shares, together responsible for 75 billion potential views on this social media, and 9.6 million actual clicks to 59,088 unique resources. We design a reproducible methodology and carefully correct its biases. As we prove, properties of clicks impact multiple aspects of information diffusion, all previously unknown. (i) Secondary resources, that are not promoted through headlines and are responsible for the long tail of content popularity, generate more clicks both in absolute and relative terms. (ii) Social media attention is actually long-lived, in contrast with temporal evolution estimated from shares or receptions. (iii) The actual influence of an intermediary or a resource is poorly predicted by their share count, but we show how that prediction can be made more precise.