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 <TD <PARAM1 <PARAM2>>>)
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