For a GAM this summary is not that important, particularily your sample size is rather large given the relatively simple model (p-values should not be relevant). Plot the data together with the model prediction and check if the fit is reasonable and if it helps to identify interesting patterns (you might then develop/generate hypotheses about the reasons for such patterns occuring and plan future experiments/studies to test these hypotheses).

The summary should be understandable when you know what a GLM and a GAM is and what spline is and how they are evaluated. If you don't know the theory behind (that cannot be explained here, but you should find plenty of literature), the output will remain somewhat cryptic.

Although that should also be clear, it's maybe good to note that R's model formulas include a default intercept term, so your model cvd ~ s(temp) is actually cvd ~ 1+ s(temp). The intercept is the predicted value given all other variables (that is, temp) are all zero (that may or may not be of interest, depending on your model, how the variables are coded/operationalized and on your questions.

The s(temp) term is a spline function of the temperature, allowing the model to fit a smooth curvy relationship between temp and cvd. The summary shows the results of an approximate analysis of deviance, where the likelihood of the data under the model cvd~1+s(temp) is compared to that of the restricted model cvd~1. Under the larger model, the difference in log-Likelihoods is approximately Chi²-square distributed, therefor the "Chi.sq" value (with corresponding p-value) is given. The tiny p-value indicates that your data is sufficient to resognize that some wiggely relationship between cvd and temp explaines the data better than assuming that cvd is independent of temp -> "intercept-only model"; the intercept is the log(mean cvd).

I would just add two more comments to Jochen's answer:

1. You can run some diagnostics using gam.check(model1) and also plot the model with plot(model1). The latter will give you a visual that may help you interpret the relationship between temp and cvd. However, I notice that the deviance explained is 1.68% (see the second to last line in the summary output); since this is so low, the relationship between these two variables may be very weak, or there may be some other issues with the model (the diagnostics can give insights here).

2. You ask "what these parametric coefficients ... mean?" I will just reiterate that GAMs are different from GLMs in that there are no linear coefficients (betas) to interpret.

The key is a three element plot for each predictor variable:

a plot lot of the partial residuals;

the obtained smooth;

the confidence curve around the smooth.

for me the whole point of a Gam is as an exploratory graphical procedure; see

Article “Moving Out of the Linear Rut: The Possibilities of Generali...

Article Generalized Additive Models, Graphical Diagnostics, and Logi...

They are from the early days of this technetium and they were deliberately written to be expository. The second paper considers a Logit/Bernoulli model which is very close in the family of models to your Log/Poisson.

To plot the smooth-terms (model prediction, as mentioned by Jochen Wilhelm , you can use the ggeffects-package (http://strengejacke.github.io/ggeffects). Here is an example code:

library(mgcv)

library(ggeffects)

set.seed(2) ## simulate some data...

dat

(related publication: Article ggeffects: Tidy Data Frames of Marginal Effects from Regression Models