An assertion is a declaration that's made emphatically, especially as part of an argument or as if it's to be understood as a statement of fact.
To assert is to state with force. So if someone makes an assertion, they’re not just trying out an idea — they really mean it. An assertion can also be an act that seems to make a statement without words. When your dog urinates in multiple places up and down your block, he's making an assertion of his dominance (also called "marking") over his "territory."