There are many things I like about Mark Knopfler's work, both his solo albums as well as Dire Straits:
Personal Geography
The way he weaves memories from his own life (even seemingly mundane things) brings a personal connection to his music. For example, taking the train in Southbound Again, remembering working with Basil Bunting at the Evening Chronicle when he was (briefly) a reporter, hearing the Sultans of Swing perform in a pub in Deptford, listening to employees chatting in an electronics store (Money For Nothing), and of course reflecting on his career recently in Matchstick Man.
Poetic Lyrics
The lyrics in his songs are so often very poetic; a recent example is One Song At A Time (referring to his friend Chet Atkins saying how he picked his way out of poverty one song at a time) with imagery like the "In a taproom lined with mirrors there's a man there at the bar..." and "any more poor old fakers trying to dance in my old shoes, I'll be gone over the ocean with the transatlantic blues". A more classic example is of course the imagery and emotion in Romeo and Juliet (again also based on events from his life). He also writes songs that tell a story with vibrant imagery, such as Heart Full of Holes or Done With Bonaparte.
What is remarkable about his songs is it's like a form of poetry that has many layers - you can enjoy the music, you can enjoy the lyrics and melody, or you can listen to the deeper meaning behind the song (such as his life in a song like Basil or a metaphor in a song like Old Pigweed)
Metaphors
A number of his songs include powerful metaphors, such as Old Pigweed, Quality Shoe, What It Is, Cannibals, The Bug, My Bacon Roll, etc. This adds real depth in that these aren't just songs with great guitar work or are entertaining, but ask deep questions too.
Errata
I haven't liked some of his recent albums as much due to their heavy Celtic/Country feel, but I really liked Down The Road Wherever as it returned to a bit of of a rock sound (and even funk). I wrote in more detail about it here.
Conclusion
In closing, in interviews Mark Knopfler said that he most enjoys songwriting because of how it takes on different meanings for those who listen to it (and often times not what the original meaning was to him). Thank you Mark for sharing these musical gems with the world!