“My heart leaps up” (Line 1) is an idiom not meant to be taken literally but expresses a truth: When a person is suddenly filled with joy, their heart—often thought of as the seat of emotions—feels like it is rising upward. The converse may also be true, as the expression “my heart sank” demonstrates.

The cause of the sudden elevation in the speaker’s mood is the sight of a “rainbow in the sky” (Line 2). This commonplace natural phenomenon—a beautiful multicolored arc stretching across the sky—can appear suddenly, as if from nowhere, capturing the imagination of the observer. Often, the sight of a rainbow produces wonder and even awe—a feeling Wordsworth emphasizes.

Wordsworth often celebrated his own past; he was especially drawn to his childhood, when his love of nature was purest and most uncomplicated. In Line 3, he looks back to these early days “when life began”; he remembers how much his heart jumped then whenever he saw a rainbow. He still reacts the same way in the present, “now [he is] a man” (Line 4). Despite the many transformations that come with the growth from boy to man, Wordsworth finds the