People invest time, attention, and emotion while engaging in various activities in the real-world, for either purposes of awareness or participation. Social media platforms such as Twitter offer tremendous opportunities for people to become engaged in such real-world events through information sharing and communicating about these events. However, little is understood about the factors that affect people's Twitter engagement in such real-world events. In this paper, we address this question by first operationalizing a person's Twitter engagement in real-world events such as posting, retweeting, or replying to tweets about such events. Next, we construct statistical models that examine multiple predictive factors associated with four different perspectives of users' Twitter engagement, and quantify their potential influence on predicting the (i) presence; and (ii) degree - of the user's engagement with 643 real-world events. We also consider the effect of these factors with respect to a finer granularization of the different categories of events. We find that the measures of people's prior Twitter activities, topical interests, geolocation, and social network structures are all variously correlated to their engagement with real-world events.