Pad printing is a relatively new printing process compared with screen printing and letterpress. It developed when it was possible to make printing pads out of silicone rubber, and has seen substantial growth over the past few decades.
Silicone rubber repels many substances (including ink), and by moulding itself to any given object, allows you to print on uneven surfaces. You can print on irregular surfaces, on sloping and vertical surfaces, with more than one side simultaneously.