Like all heraldic coat of arms, almost every component of the Manchester Coat of Arms has a symbolic meaning. At the centre of the shield (in a shape known as '13th-century', which Manchester chose for reasons unknown), the three diagonal stripes represent the three rivers of Manchester: The Medlock, The Irwell and The Irk.
The ship at the top of the shield represents the trading relationships of Manchester, and above the shield the terrestrial globe covered in bees also has significance. The bee in heraldic terms represents efficient industry, and to this day the bee is often used as a shorthand emblem of Manchester and can be see on many street bollards around the city centre.
The heraldic antelope with its gold chain represents the engineering industries. The lion's crown is a castle, a reference to the ancient Roman fort of Castlefield: the first known civilised settlement of Manchester. The red roses they each wear on their shoulders are references to Lancashire, a symbol that is still used widely today to represent the county Manchester historically belongs to.
The motto can be loosely translated as 'Wisdom and Effort' although some prefer to read it as meaning something along the lines of 'Think about the consequences of your work before beginning it'.