द्वा सुपर्णा सयुजा सखाया समानं वृक्षं परिषस्वजाते । तयोरन्यः पिप्पलं स्वाद्वत्त्यनश्नन्नन्यो अभिचाकशीति ॥१॥
III-i-1: Two birds that are ever associated and have similar names, cling to the same tree. Of these, one eats the fruit of divergent tastes, and the other looks on without eating.
समाने वृक्षे पुरुषो निमग्नोऽनिशया शोचति मुह्यमानः । जुष्टं यदा पश्यत्यन्यमीशमस्य महिमानमिति वीतशोकः ॥२॥
III-i-2: On the same tree, the individual soul remains drowned (i.e. stuck), as it were; and so it moans, being worried by its impotence. When it sees thus the other, the adored Lord (Ishwara), and His glory, then it becomes liberated from sorrow.
Here the 2 birds are Jivatma (Individual Soul) and Paramatma (Universal Soul).
Fruits- Material Desires.
So, in simple word, the verse means, in the material world 2 Parameshvara and Jiva remains together, where Parmeshwara remains independent of Maya and just witnesses everything but jiva remains stuck in Maya and experience both happiness and sorrow again and again means stuck in the cycle of life and death, till it realises the Parmeshwara. And after realising Brahman the Jiva becomes Brahman itself and gets moksha.
For more, you can see this answer of mine.
I hope this clarifies your queries.