According to Linda Elder and Richard Paul, "An implication is that to which our thinking is leading us. When you say things, you imply certain other things. For example, if you make a promise, you imply that you will keep it" (The Aspiring Thinker's Guide to Critical Thinking, 2009, p. 28). In academic research, you should consider the implications of what your sources are saying. You should also consider the implications of your own arguments.
Research involves critical interaction with information sources. Don't just accept an argument because it seems correct on the surface or because it matches your point of view. Instead, think through the implications of the argument. What would it mean to accept this argument? What effects would it have? What are the implications and/or consequences of agreeing or disagreeing with this argument?