prolonged unfulfilled desire or need
"After years of working abroad, she felt a deep longing for her childhood home and the quiet evenings spent on her porch."
An earnest and deep, not greatly passionate, but rather melancholic desire.
"She sat by the window, her eyes filled with a quiet longing for the summer days that had long since passed."
present participle of long
"She felt a deep longing for home as she watched the last train disappear into the night."