The phrase "to produce an effect" means to cause something to happen or have an impact on something else. It refers to the ability or action to create a result or outcome. Full definition
You may notice that even these brief thought experiments produce effects in the physical emotional, and breath layers of your greater being. (Em-powerYoga.com)
A second implication involves a reversal of our ordinary understanding that causes produce effects. (religion-online.org)
The relationship between a physical cause and its effect is contingent in the sense that it only exists if the cause actually produces its effect. (faith.org.uk)