The day-age theory is another attempt (like the gap theory) to accommodate evolution into Christianity. Instead of adding millions of years to earth history before the Biblical account of creation, the day age theory expands the length of the days into long ages, each millions of years in length.
This idea has had appeal for many people but it is obvious that the events described in Genesis are not the same as the millions of years in the evolution scenario. For example, the sun, moon and stars were not created until day 4 as per Genesis, but according to the long ages view, the earth would have appeared long after the sun and other galaxies and stars.
Another problem is the Bible’s treatment of the Hebrew term “yom” or “day” in Genesis chapter 1. Hebrew grammar supports use of “yom” in Genesis 1 as meaning a 24 hour normal day. The passage 2 Peter 3:8 is sometimes quoted to suggest that long time intervals can possibly be applied to the word “day”, but the context of the passage is different. Moreover, Exodus 20:11 supports the understanding of “yom” as a normal 24-hour day.
For these and similar reasons, the day-age theory has also largely been abandoned by Christians.