What does the Ghost of Christmas Present mean when he shows Scrooge the miners and says, "But they know me. See!"?

In this chapter, the Ghost of Christmas Present visits Scrooge and shows him what is happening all around him at the present time. In addition to taking him to a bustling marketplace full of food, and to the Cratchit residence where Scrooge sees his employee's many children, including Tiny Tim who is ill and uses crutches, the Ghost brings him to a desolate landscape. 

"What place is this?" asked Scrooge.

"A place where Miners live, who labour in the bowels of the earth," returned the Spirit. "But they know me. See." 

A light shone from the window of a hut, and swiftly they advanced towards it. Passing through the wall of mud and stone, they found a cheerful company assembled round a glowing fire. An old, old man and woman, with their children and their children's children, and another generation beyond that, all decked out gaily in their holiday attire. The old man, in a voice that seldom rose above the howling of the wind upon the barren waste, was singing them a Christmas song -- it had been a very old song when he was a boy -- and from time to time they all joined in the chorus. So surely as they raised their voices, the old man got quite blithe and loud; and so surely as they stopped, his vigour sank again.

In this scene, Scrooge is shown a group of people whose daily lives are desolate and difficult (miners work underground and often live short lives due to the dangers of their jobs, ranging from accidents to health problems from inhaling coal dust). The Ghost shows him that such people nevertheless celebrate the Yuletide season with joy; they dress in their finery and sing around the fire. 

It could be said that the old man seen here is a stand-in for Scrooge  himself; the old man sings a song to the children, and when they join in on the chorus he becomes more happy and animated. The children invigorate him, much as Scrooge finds that his heart goes out to Tiny Tim, and is moved by his loving disposition, despite the boy's illness.

The Ghost makes a point that even these people whose lives are harsh can "see him"--this means they know how to find the joy in their lives every day, and savor the moments of happiness when they come. This is something Scrooge has not done in many years, and this Ghost's lesson for him is to "seize the day" and enjoy every moment for what it is, not worrying about money or focusing on small unpleasant tasks or annoyances. Scrooge takes this lesson to heart when he tries his best at the end to improve the lives of people around him, especially Bob Cratchit and his family.