A cycle is a loop. A graph is cyclic if you can find at least one path starting from one node and going back to that exact same node.
As you can imagine, it's important to be aware of the presence of cycles in a graph, since they can create infinite loops in a graph traversal algorithm, if we do not pay enough attention to it. The following image shows an acyclic graph versus a cyclic graph:
All those properties are not self-exclusive and can be combined. Especially, we can have directed acyclic graphs (DAG), which usually behave nicely.
