Low profile furniture is not the same as keeping a low profile in the common vernacular. Low profile furniture is much more literal in that the height of the furniture is less than you might find in more traditional furniture. Low profile furniture is typically used in modern and contemporary spaces.
Modern and contemporary spaces may have a lower sight line in the room. Focal points like fireplaces may be lower to the ground as well. In this loft, the windows are very tall. The low profile seating fits underneath the windows and do not interrupt the view. Low profile furniture can also help ground a space with a vaulted ceiling as well as accentuate the vertical volume in the room.
Low profile furniture is also typically more streamlined than traditional forms. Clean lines and a lack of flourishes and ornamentation make these pieces work well in lofts and mid-Century modern homes. A solid colored rug that adds texture is a great fit for a modern space. What details are left, a curved leg or button tufting on the back of the sofa, become stronger elements in the overall design.
Keeping low profile furniture on the same plane is important to the overall unity of the design. In this living room the sofa, right side table and coffee table all stay below a certain line. You may not want table as shown on the left, as it is a little too high for the sofa. Having to reach up to set down your glass or book can be awkward.