Most people hope that the traffic to their website will grow over time. The natural way for this to happen is for people to discover the site, like it, and spread the word about it in various ways. Of course such growth can happen at different rates, depending on the site's niche and the degree of general interest in the topic. The "snowball effect" usually refers to cases in which the growth is exponential. But even exponential growth can happen at different rates, even rather slowly. Of course a site's traffic can't grow exponentially forever, since the population of the earth is finite.
Occasionally someone here at WebmasterWorld mentions that Google's algorithm might take account of the rate of backlink acquistion in proportion to a site's traffic. For example, A site that gets very little traffic can't be expected to rapidly acquire lots of new "natural" backlinks [This assumes that no artificial "link-building" takes place]. This also applies to social button signals, etc. So if everything happens naturally, there should be a correlation between the amount of traffic a site gets and the rate of backlink and social signals growth.
Exponential growth in traffic (the snowball effect) will occur if visitors to a site tend to spread the word in ways which, on average, bring in a steady number of new visitors. Thus the more visitors it already has, the more new visitors it will gain, in proportion.
In most cases Google can use its Chrome browser to get a good estimate of a site's traffic and rate of growth. If traffic is growing, the cause needs to be determined. For example, traffic growth due to increased Adwords spending should to be discounted.
Snowball-type growth is probably more likely to happen with some types of sites than with others. Also, there's a big complication, because changes in Google's own rankings for a site can have a strong feedback effect on its traffic, since Google is so dominant in search. On the other hand, if a snowball effect is occurring, Google's algorithm might take it as a positive signal. Then the resulting rankings improvement would reinforce the snowball effect, and maybe even accelerate it.