r

As not_bonferroni mentions, help(summary.gam) do have useful information. Do see the references therein or

Wood, Simon N.. Generalized Additive Models: An Introduction with R, Second Edition (Chapman & Hall/CRC Texts in Statistical Science).

particulier section 6.12. To give a brief and simple answer to

When I take a summary of the model, I get a chart that indicates the "significance of smooth terms" (which is quite significant). What does this represent?

let us suppose that you only have one covariate $x_i$ and you have an outcome variable is $y_i\in\{0,1\}$ which is $1$ if observation $i$ is overall happy and $0$ otherwise. The model you fit is

$$ g\left(E\left(y_i \mid x_i\right)\right) = \alpha + f(x_i) $$

where $g$ is a link function, and $f$ is an unknown smooth function. Then the $p$-value is for the null hypothesis $H_0:\, f(x_i)=0$. To give a simple example then we make some simulations below where $f(x_i)=2\sin(x_i)$, $f(x)=x$ and $f(x_i)=0$.