Ladder logic or the Ladder programming language is a method of drawing electrical logic schematics. It is now a graphical language very popular for programming Programmable Logic Controllers (PLCs). It was originally invented to describe logic made from relays. The name is based on the observation that programs in this language resemble ladders, with two vertical "rails" and a series of "rungs" between them. In Germany and elsewhere in Europe, the style is to draw the rails horizontal along the top and bottom of the page while the rungs are drawn sequentially from left to right.
A program in ladder logic, also called a ladder diagram, is similar to a schematic for a set of relay circuits. Ladder logic is useful because a wide variety of engineers and technicians can understand and use it without much additional training because of the resemblance.
Ladder logic is widely used to program PLCs, where sequential control of a process or manufacturing operation is required. Ladder logic is useful for simple but critical control systems, or for reworking old hardwired relay circuits. As programmable logic controllers became more sophisticated it has also been used in very complex automation systems.
Ladder logic can be thought of as a rule-based language, rather than a procedural language. A "rung" in the ladder represents a rule. When implemented with relays and other electromechanical devices, the various rules "execute" simultaneously and immediately. When implemented in a programmable logic controller, the rules are typically executed sequentially by software, in a loop. By executing the loop fast enough, typically many times per second, the effect of simultaneous and immediate execution is obtained.
The most common components of ladder are contacts (inputs), these usually are either NC (normally closed) or NO (normally open), and coils (outputs).
Of course there are way more components to a full ladder language, but understanding these will help grasp the overall concept.
The ladder consists of one or more rungs. These rungs are horizontal traces, with components on them (inputs, outputs and other), which get evaluated left to right.
This example is the simplest rung: 
The input on the left, a normal open contact is connected to the output on the right Q0. Now imagine a voltage gets applied to the leftmost end, as soon as the B0 turns true (e.g. the input is activated, or the user pushed the NO contact), the voltage reaches the right part Q0. As a consequence, the Q0 output will turn from 0 to 1.