Why do we human use a base-10 numeral system, while a computer uses a base-2 one? A common explanation is: because we are born with a natural counting tool - ten fingers! If we have 16 fingers, we might be using the base-16 numeral system right now. Imagine seeing price tags labeled "14A8" in an Apple Store. Crazy, huh? But a computer uses transistors to compute. Since the transistors can only have two statuses - on (high) and off (low), it would be easier for a computer to use a binary system.
What are number systems after all? A numeral system is a writing system for expressing numbers, that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations (cited from Wikipedia: Numeral System). And a binary number is a number expressed in the binary numeral system, or base-2 numeral system, which represents numeric values using two different symbols: typically 0 and 1 (cited from Wikipedia: Binary Number).
How to convert the binary number 11011011 into a decimal number? In a binary system, the digit to the very right represents a 1 = 20 and the second right digit represents a 2 = 21, the third a 4 = 22... So the binary number (11011011)2 = 1 + 2 + 8 + 16 + 64 + 128 = (219)10.