As mentioned before, elections deliver a mandate and therefore lend legitimacy to the ruling party. Also, if individual deputies from small parties are co-opted into decision making, for example, as part of a national governing 'Front' or as experts on a committee, then these members -- and their parties -- could begin to identify more strongly as 'insiders' (even with minimal influence) and be reluctant to genuinely oppose the system they are part of. This too can protect the ruling party. It also allows the ruling party to claim that government is representative.

In a dominant party system exist two possible scenarios depending on the established electoral rules: there would be those systems where the reality of dominance of one party is the result of a cast of real preferences of the population, but where the established rules would envisage that the result was different and the predominance of a given party could lose by a chord electoral process with established rules; in that case, dominance is a planned and not essential to the rules situation. In this case, the system could be properly democratic, where minorities could eventually conventirse majorities and elections fujarían perióricamente the function of allowing this may occur, although not happen. The elections, however, would be playing a defining role of the weights of the political forces and location of certain forces in conditions that could bring them later to wield majority status or the possibility of forming the government. Another situation would be that the dominance of one party is the direct result of electoral rules established and if so would effectively into question the democratic character of the system, because not comply with the rule that minorities may eventually become majorities; in this circumstance, the elections would act only as a process of legitimation of the majority and eventually allow the strength of the opposition, they would have to fight not only or mainly to achieve greater voación, but by creating the conditions for reform is expressed of electoral rules that become properly democratic, allowing minorities to meet the conditions to form a government or become majorities.

Although related to my interests it is not a discussion I closely follow. I know there is a relative large discussion on electoral authoritarianism but these two articles have helped structure my own thoughts on the issue.

Magaloni, B. 2008, "Credible Power-Sharing and the Longevity of Authoritarian Rule", Comparative Political Studies, vol. 41, no. 4-5, pp. 715-741.

Roberts, T.L. 2015, "The Durability of Presidential and Parliament-Based Dictatorships", Comparative Political Studies, vol. 48, no. 7, pp. 915-948.

Very good responses provided, but to interpret your question is terms of "essence", I would, in a single sentence:

Elections in a dominant party system provide a mechanism for legitimizing that governing authority.