The laws of physics and mathematics dictate that all electronic systems are subject to background 'noise' in their transmission and reception. It's been found that biological systems which involve electrical and chemical signals between neurons are also inherently quite 'noisy'.

The neuronal noise levels can be measured in the laboratory, and are usually around ten to twenty times (10dB - 20dB) lower that the 'actual' signal.

There are several theories attempting to explain the prevalence and extent of noise in neuronal networks ref.but no general agreement. The noise probably has a range of sources.

Until the 1990s, neurologists had generally assumed that (as in human-built systems) signal noise would make reliable neural communication more difficult, and that there is likely to be some kind of filtering system in operation to 'clean-up' the nerve signals. If there is such a system, it's currently unknown how it operates.

But research beginning at the end of the 1990s began to suggest that the noise might actually benefit neuronal systems rather than being detrimental.

A news article in Nature Neuroscience, Volume 9, Issue 11, entitled'Noisy neurons can certainly compute' explains :^{[ paywalled ]}

Mathematically, the rules for calculating optimal probabilistic estimates are known as Bayesian inference, and psychophysical experiments show that, under various laboratory conditions, human performance in simple tasks that require the combination of uncertain cues is essentially as good as it can be given the available information.
Such optimal performance indicates that the brain must implement some form of Bayesian inference, but so far, how this happens has remained unclear. The new paper by Ma and colleagues shows that the variability of cortical neurons has a form that greatly simplifies one of the critical operations in this process, the pooling of individual cues.

Ma and colleagues ref. Bayesian inference with probabilistic population codes ^{[ paywalled ]} Nature Neuroscience, Volume 9, Issue 11

As mentioned above, it's still unclear to what extent, and by what means, signal noise may be a hindrance or a benefit to neuronal systems.