ngspice simulation : random signal source
It's just in the manual
:


  4.1.8 Randomvoltagesource
  The TRRANDOM option yields statistically distributed voltage values, derived from the ngspice random number generator. These values may be used in the transient simulation directly within a circuit, e.g.  for generating a speciﬁc noise voltage, but especially they may be used  in the control of behavioral sources […] to simulate the circuit dependence on statistically varying device parameters. A Monte-Carlo simulation may thus be handled in a single simulation run. 


You should read the line as follows:

Vn 1 n1 dc 0V ac 1mV trrandom(1 5us 0s 125m 0m) 
--
name of voltage source

Vn 1 n1 dc 0V ac 1mV trrandom(1 5us 0s 125m 0m) 
   ----
nodes the voltage source is connected to

Vn 1 n1 dc 0V ac 1mV trrandom(1 5us 0s 125m 0m) 
        -----
type and value of voltage source for transient analysis

Vn 1 n1 dc 0V ac 1mV trrandom(1 5us 0s 125m 0m) 
              ------
AC amplitude for ac analysis

Vn 1 n1 dc 0V ac 1mV trrandom(1 5us 0s 125m 0m) 
        +++++        --------------------------
adds statistically distributed voltage values to the DC of 0V (the +++ part)


According the specification of TRRANDOM(TYPE TS &lt;TD &lt;PARAM1 &lt;PARAM2&gt;&gt;&gt;) in your example  


the noise is uniformly distributed
the duration of an individual voltage value is 5 us
time delay parameter is not used
the noise has an amplitude of 125mV
the noise has an offset of 0mV