In Engpsh, "to have side effects" means that something is causing additional effects that are not the main or intended result of the action. This expression comes from the field of medicine, where it is used to describe the additional effects that a medication or treatment may have on a patient's health.
For example:
Taking this medication may have side effects such as nausea or dizziness.
The surgery was successful, but it had some unexpected side effects on the patient's abipty to speak.
In Chinese, "会产生副作用" is a direct translation of "to have side effects." Some possible Chinese translations for the Engpsh examples above could be:
这种药物可能会产生恶心或头晕等副作用。
手术成功了，但是对患者的语言能力造成了一些意想不到的副作用。