Definition
Irrelevantly, off-topic.
Origins
First appeared in the 10th century with literal meaning "by the side of the road", from Old English weġ (which became "way") meaning "road". Soon afterward (circa 1000) it came to mean "during one's journey". The figurative meaning developed in the mid-16th century, with the first instance of the modern meaning being from 1614.
How People Actually Use It
"oh, and On that note," or "While we're on the subject" or "since you mentioned it" or "Concerning that,"
"I can not wait to see you at Thanksgiving, Karolina. By the way, will you be eating the delicious pie I make?"
Source: Urban Dictionary