A Google search tells me that "channel letters" are "custom-made metal or plastic letters commonly used in exterior signage on public and commercial buildings, and often internally illuminated" (https://en.wikipedia.org/wiki/Channel_letters ). When you're looking at a a big, flat object that is oriented vertically--like a sign on a wall--the three dimensions are often given the names height, width, and depth. As you are standing, looking at the object, height means up and down, width means to the sides, and depth means closer and farther away from the observer. In the case of a sign hanging on a wall, in everyday language we might call it either "thickness" or "depth." The "depth" of a channel letter would be a dimension--in the U.S., often in inches. The Wikipedia article tells me that channel letters used to be 5" to 6" (12.5 to 15 cm) in depth. They would have projected that far from the wall. Now, because of LED lighting, their depth can as little as 2" to 3" (5 to 7.5 cm). The depth is less. The word for "less deep" is "shallow." Channel letters are becoming "shallower." They have a "shallower depth." A Google search shows that the phrase "thinner depth" is also used, and that letters with a shallow depth are also called "low profile" letters. P.S. In the case of a lake or ocean, "depth" can mean extent up and down. We say "the ocean is deep." We can say "the depth of the Gulf of Maine reaches 500 m. in places." And we can say "As we sail from the Gulf of Maine into George's Bank, we are sailing into shallower depths."

Difficult to know without more context. What are the "channel letters" they are referring to? My guess is that "shallower depth" means they are making the electronics smaller.