"Make sure you can maintain a sense of rhythmic urgency without a metronome going."
Practicing with a metronome is essential for any musician serious about playing with great rhythm.
Practicing without a metronome is also essential for any musician serious about playing with great rhythm.
Let me explain...
To improve at anything on your instrument you must enter a feedback loop. That means getting precise data about what is actually coming out of your horn, using that data to try something a little different and then getting more data.
Lather. Rinse. Repeat.
In this case, that means using a metronome and a recording device to figure out whether you are playing perfectly in time. And if not, noticing the patterns of how or where you are playing with bad rhythm so you can adjust accordingly.
But some players fall into a trap of practicing with a metronome all the time (or darn close to it.) While this might seem like a good idea, it is actually a really bad idea. You never want to come to rely on a tool that won't be present when you are performing or auditioning.
The way to properly use a metronome is to record yourself both with it and without it to see if you can play with great time regardless. It should be used as a reference point, not provide the rhythm for you.
So there are two types of people who can fall into the lack of rhythmic urgency without a metronome trap that David Zerkel alluded to in the above quote, those who never use a metronome and those who use one too much.