What might Tennyson have meant by the region of shadows and the region of realities in the poem "The Lady of Shallot"?
I'm not sure if we can really make this distinction in Tennyson's "The Lady of Shalott." After all, the island where the lady exists is located on a river that flows down to Camelot. Camelot, of course, was the mythical setting of Arthurian romance and thus not entirely "real." However, the use of the mirror and the notion of shadows also suggests that Tennyson, who was classically educated, might be creating a parallel with Plato's allegory of the cave.
The world outside the tower is less unreal than the one in the tower. Outside the tower, people engage in ordinary activities such as farming, weddings, and funerals. The Lady of Shallott appears to be ageless and immortal (until the curse is triggered) and has no need of sleep as she weaves both night and day. She also seems not to eat or engage in any other normal human activity except for her weaving. The Lady herself is described using the terms "fairly" and "angel" and thus is somehow otherworldly.
One can read the tower world as that of art and the imagination. The Lady is creative in that she sings and weaves. When she leaves that world and acts rather than imagining, she dies. This reading would cohere with several of Tennyson's other poems.
Another possibility is to read this as a poem about the destructive nature of love, which is again a common theme in Tennyson's so-called "girl poems." At first, the Lady is untroubled by passions and content, but when desire and passion enter her world, she dies.
There are many possible answers you might receive to this question and various critics have debated what the realm of shadows where the Lady of Shallot lives, and what the realm of reality, into which she momentously enters, might actually symbolise, with such answers as art and life. However, my own feeling, for what it is worth, is that this poem is all about the contrast between life and the pale reflection of life or death in life.
Note the way that the Lady is shown to live in a world of shadows and greys, which even dominate the "four grey walls and four grey towers" that make up her abode. She is a character who is divorced from life, symbolised in the bright colours of the villagers that she watches go up and down the road. However, life and its spirit is most famously and forcefully captured in the character of Sir Lancelot, who enters with movement and colour, described as a "bowshot." His "brazen greaves" are emphasised and adjectives such as "dazzling" and "sparkled" are applied to him. It is this sight that gives the Lady the courage to defy the curse and to try and start living, which of course has tragic consequences. Participation in life is definitely attractive and tempting, but participating in life will always have its consequences, some of which can be fatal.