These are called medullary rays and become pronounced when the oak is quarter sawn. Usually considered decorative, especially when they are displayed on the whole piece, and authentic to oak furniture built prior to WWII. After that, flat sawn lumber which didn't display medullary rays was used to save money and conserve wood. A table leg of oak, with four flat sides would usually display two sides featuring medullary rays and two sides not.

Someone2010's got this one nailed. Quarter sawn white oak was a characteristic of Arts & Crafts or Mission-style furniture, typified by G. Stickley and contemporaries.

Below is a photo of this. It will only get more prominent with a stain or finish on it.

Here is a link that might be useful: {{gwi:1522863}}