A spurious effect is an (statistically significant) effect between two variables for which no logical (theoretical) explanation can be found.
In quantitative research many statistical analyses are conducted. Most of these should be in accordance with a theoretical framework. Sometimes however a statistical result is significant while there is no logical explanation for it. How can the number of branches on trees be connected to the number of cars in the department in a town? This looks peculiar to me and very odd. So this is a spurious relationship.
Be careful if you want to explain spurious relationships. It might be bias, and remember, statistics are based on arithmetic and explanations are based on theories. They are two different levels of thinking. It’s like trying to explain why a calculator sometimes calculates 2 + 3 = 7. If it happens only once, it is a curiosity. If it happens over and over, maybe a confounder can be found. In that case try to figure out what that confounder might be, and use hierarchical regression or a form of mediation to make this spurious relationship disappear.
When I kept thinking about my example of the relationship between the number of branches and the number of cars, some explications came up. Maybe it has to do with the wellbeing of the neighbourhood, the maintenance of the trees or the number of kids in the neighbourhood. But of course, these explications are for now only wild ideas.