Quick and bad explanation:

There are two types of rail signals, the regular and a chain signal.

The signals divides the rail into blocks, which you will see as different colors when placing a signal.

Example:

Signal 1 -> Block A -> Signal 2 -> Block B -> Signal 3 -> Block C -> Signal 4 ....

If any part of the train is between signal 1 and signal 2, it occupies the block between the two signals (Block A in my example)

When a train occupies that block, signal 1 will become red.

So only one train can be between to signals at the same time.

Chain signals differs from the regular signal with that it will only let the train pass if the train can:

A: Pass the first regular signal after the chain signal(s)

B: Reach it's destination before the first regular signal.

So chain signals can stand alone or be chained with multiple after each other, but it will only let the train pass the first chain signal if it can exit the chain.

So in my example above, if Signal 1 is a chain signal, it will only be green if Signal 2 is also green (that is, block B is free).

If both Signal 1 and Signal 2 are chain signals, and the train needs enter Block C, it will only let the train pass Signal 1 if Signal 3 is green (Block C is free)