An upright piano, or vertical piano, is a piano whose frame is vertical instead of horizontal. There are many different sizes, so if you are purchasing a new piano, you should always check the manufacturer's specifications to find out what that particular piano's dimensions are.
Modern pianos are loosely grouped into four categories determined by their size. A spinet model is the shortest, and the strings are located below the keyboard instead of above. Next is the console piano. Its strings are above the keyboard, but they are shorter than full-length. A studio piano is the shortest piano that can still house full-sized strings above the keyboard. These are usually between 42 and 45 inches high. The tallest piano is called an upright, and it can be any reasonable height.
Vertical pianos are typically 20 to 25 inches in depth and 55 to 60 inches in length. There is more variance in height. A professional-quality piano is likely to be of studio height or upright height, so it will be at least 42 inches in height.
Grand pianos are classified by length, and always take up more space than upright pianos. A concert grand is often 9 feet long. A parlour grand may be 7 feet. A baby grand is the smallest and is generally about 5 feet long.
Older pianos have far more variance than contemporary pianos, but by and large, they tend to be taller. Whatever piano you are considering, you will need to get exact dimensions for that piano to know for sure.
One early type of upright piano was called a "birdcage piano" because its dampers seemed to suggest a birdcage. There are many shapes and sizes of pianos that are no longer made today.