"Serious implications" means that something has significant and important consequences or effects that need to be considered and taken seriously. Full definition
Scientists expect the rate of melting to accelerate, with serious implications for future sea level rise. (ucsusa.org)
As you no doubt know, acts of animal cruelty are often the predictors and indicators of escalating violence against the human members of the family, with serious implications for society as well. (tulsapetsmagazine.com)
The lack of responsibility and understanding of how serious the implications of neglect is simply astounding. (humblemechanic.com)