悠 appears in many common compounds: 悠久 (long-standing), 悠闲 (leisurely), 悠然 (carefree), 悠扬 (melodious, of sound carrying far). When doubled as 悠悠, it emphasizes the leisurely or drawn-out quality.
memory
The character 悠 has 心 (heart) at the bottom — a heart that takes its time, unhurried and at ease.