The significance of bounded parameters in complexity
When you see that a parameter is bounded, you shouldn't think of the value of the parameter of a single graph, but of a class of all graphs that satisfy the bound on the parameter.

So, to say that graph isomorphism is in polynomial time for bounded degree graphs really means that, for every $d$, there is a polynomial time algorithm&nbsp;$A_d$ that decides graph isomorphism on the class of all graphs of degree at most&nbsp;$d$.  However, the running time of&nbsp;$A_d$ depends on&nbsp;$d$.

And, yes, the take-home is generally that there are decent algorithms as long as the parameter is small. What counts as decent will depend on your circumstances: what sorts of inputs you need to deal with and how much computing time you have available.