Speaking on the record's title-track "4:44," JAY-Z revealed the following:
'4:44' is a song that I wrote, and it's the crux of the album, just right in the middle of the album. And I woke up, literally, at 4:44 in the morning, 4:44 AM, to write this song. So it became the title of the album and everything. It's the title track because it's such a powerful song, and I just believe one of the best songs I've ever written.
But aside from JAY'z 40/40 Club franchise, he and wife Beyoncé have a long and fascinatingly coincidental history with the number 4. JAY and Bey were both born and married on the 4th, on December 4th, September 4th, and on April 4th respectively, and even their child's first name is the phonetic pronunciation of the roman number IV (Ivy).
The pattern goes even deeper though, as explained by Complex, where you can read the full story.