The Well of Miriam

A well is a deep hole in the ground filled with water.

The ground is the representation of the physical. It is the source of the human body. 

Water is pure pristine truthful wisdom.  It is Torah. 

The well therefore represents some sort of deep Torah found inside a person.
A deep inner truth. 

As the verse says:

״מים עמוקים עצה בלב איש ואיש תבונות ידלנה״ - “Council is like deep water in the heart of man; and the man of understanding will draw them forth.” -Proverbs (20,5)

The well of Miriam was just such a well. It was all the Torah that Miriam had to offer, and even after she died it did not dry up. 

“Miraculously” her deep wisdom was remembered and perhaps even expounded upon. 

The well of Miriam lasted the entire time in the desert. That’s what was needed; since it’s the unconscious feminine knowledge that gets us through the tough times.

There is a story, or perhaps a legend, that I once read about R’ Chaim Vital. It was said that he used to forget much of his Torah learning. One day his teacher Rabbi Yitzchak Luria, better known as the Arizal, gave him to drink from the waters of the well of Miriam.
From that day on, the legend goes, R’ Chaim Vital never forgot what he learnt. 

I can’t say I truly understand this story/legend. According to my understanding though, the Well of Miriam is practically synonymous with not forgetting your learning.
For that is the symbolic meaning of it not drying up in the desert. The ability to remember truth even in dark times. 
The ability to not forget the Torah. 

This can also shed light on another difficult story in the Torah. Namely, Moshe extracting water from rocks. 
The rock represents physicality without depth - without anything inside of it to share.
Even from such things or people, Moshe could draw out truth and deep wisdom.
He could use anything to express Torah, and in so doing, elevate anything to the divine (which is how everything can be rectified through the Tzaddik, the righteous man).

In the beginning, you might need to hit the rock. That is, the truth might need to be forced out.
That’s sometimes the way to start, and it was once the way people taught children.

But in the end it must come voluntarily. 

A person must find their own truth. 

Once a person finds their own inner truth, even in the desert - surrounded by adversity, they will be able to give forth the most pristine water.
All we can do is try to assist them. 

We must speak to the rock, not hit it.