Cognitive mechanisms involve ways people receive information, and the way people think about, interpret, evaluate and therefore act upon that information received.
From Heinström (2010):
The way a message is presented, and particularly how it is emotionally framed, influences the way people interpret, evaluate and act upon it. This cognitive mechanism is utilized in things like advertising and political campaigns.
The paper is saying that advertising and political campaigns aim use these mechanisms to their benefit.
Sometimes, there can be more than one cognitive mechanism in play. It is not necessarily just a way information is presented, which is one mechanism, but it can apply to information gained from experience (another mechanism) and/or elsewhere such as school or therapy (other mechanisms).
Cognitive mechanism of the brain during the decision making and learning process — Source: Zhou, et al. (2020).
During political campaigns, potential election candidates may use leverage techniques. For example, they may use collective and/or individual viewpoints and interpretations of past events gleaned from lobby groups etc. to get their message across.
Before, and during the campaign, the lobby groups may use the same sort of cognitive mechanism in similar formats to their advantage.
The information received during cognitive mechanisms can be via messages in marketing campaigns, from news reports, experience of certain situations etc.
Experience (or even lack of experience) of certain groups of people can influence behaviour toward those particular groups, especially when hearing negative and disparaging remarks about them.
On top of that, with information gained through experience (e.g. traumatic experiences), these mechanisms can be congruent or incongruent with the reality of the situation.
These and more are what are studied when looking at, say, cognitive mechanisms of treatment in depression (Roiser, et al. 2012) and cognitive mechanisms underlying the creative process (Gabora, 2002) as examples.
They sounded more like cognitive processes
A mechanism is part of a process just as any dictionary would define as, for example,
In a machine or piece of equipment, a mechanism is a part, often consisting of a set of smaller parts, which performs a particular function.
When you take all the cognitive mechanisms together, you will then be able to form the cognitive process(es) involved in forming memories, thoughts and ideas.
Gabora, L. (2002). Cognitive mechanisms underlying the creative process. In Proceedings of the 4th conference on Creativity & cognition (pp. 126-133). https://doi.org/10.1145/581710.581730
Heinström, J. (2010). Negative affectivity—The emotional dimension. In From Fear to Flow: Personality and Information Interaction; Chandos: Amsterdam, The Netherlands, 75-103.
Roiser, J. P., Elliott, R., & Sahakian, B. J. (2012). Cognitive mechanisms of treatment in depression. Neuropsychopharmacology, 37(1), 117-136. https://doi.org/10.1038/npp.2011.183
Zhou, K., Wei, R., Zhang, Q., & Xu, Z. (2020). Learning system for air combat decision inspired by cognitive mechanisms of the Brain. IEEE Access, 8, 8129-8144. https://doi.org/10.1109/ACCESS.2020.2964031