To entwine is to twist and tangle or weave together. When you hold hands with someone, you entwine your fingers together.
A long-haired girl can entwine flowers in her curls, and she might love it when her pet snake entwines around her arm. When you knit a scarf, you entwine different colors of yarn together. There is also a figurative way to entwine: "Ever since I met you, I knew that our lives would entwine together!" Entwine combines the prefix en-, "make," and twine, "twisted strands," from the Old English twin, "double thread."