While the first verse seems to address a loved one without specifying who, the third verse gives hints that it might be a romantic partner (via Song Meanings + Facts). 

"Hey look what a hello from a stranger turned into / Caught up in a moment like it's just us in this room," Dan + Shay sing. "All the right words at the right time / And you know 'em 'cause you know me better than anyone else / We don't need anyone else."

It makes sense that the song is more focused on romantic partners because it was inspired by Dan Smyers' wife, Abby Law. "I had the phrase 'Glad You Exist' written down in my phone," said Smyers in a video released by The Country Daily. "I always caught myself saying it to my wife, just being appreciative that she is on this planet at the same time that I'm on this planet. I brought it to Shay, and we started kicking around ideas."

Now the group's fans are asking for an acoustic version, which the duo acknowledged by sharing a bunch of tweets from Twitter with the acoustic-specific requests on their Instagram, so cross fingers that remix drops soon.