To begin to run; to start moving at speed. Also used figuratively for something starting quickly.
信号が青になると子どもたちが一斉に走り出した。
When the light turned green, the children all started running.
列車がゆっくりと走り出した。
The train began to move slowly.
彼は逃げるために突然走り出した。
He suddenly started running to escape.