This pattern expresses that something is in the process of happening, particularly when the change is gradual or ongoing. It is more formal and literary than the simple 〜ている, which is the usual way to express ongoing actions in conversation. つつある often appears in news reports, essays, or written descriptions of trends or developments. It is not used for momentary actions like 'jumping' or 'turning on a light', and it often pairs with verbs that imply change or movement, such as 変わる, 増える, 進む, or 発展する.

Because of its formal nuance, you would not use it in casual speech. For example, to say 'I am eating' you would say 食べている, not 食べつつある. But to say something like 'the world is changing' in a serious context, 変わりつつある sounds more appropriate than 変わっている, which might seem too casual or merely descriptive of a state. It is also important to note that つつある is not used with verbs that already express a continuous state, like いる (to exist) or 知る (to know).