吟诗 means 'to recite poetry' with a melodic, chant-like intonation — it's a literary activity, not just reading aloud. As a separable verb (离合词), the object 诗 can be separated from 吟 by aspect markers or modifiers: 吟了一首诗 ('recited a poem'), 吟过诗 ('have recited poetry'). It's often associated with classical Chinese poetry and traditional cultural settings.