According to legend Olwen fell in love. Her father loved her a lot (maybe too much) and said the only way she could marry her one true love was if she completed ten impossible tasks. Olwen was very clever and therefore completed them all and married her love.
Though the literal meaning of Olwen is "white footprint," there is a bit of symbolism. "The path the moon takes on water" is the more accurate meaning of the name. This name is a reflection of the Celtic view of feminine nature and the energies of womanhood. The name is also Gaelic in origin, not Welsh.
A quick note. Though the original Arthurian Legend of "Culhwch and Olwen" is Welsh, and is perhaps the most famous occurrence of this name, the name Olwen is originally Gaelic.