What does the p-values besides the edf means in generalized additive model (GAM) mean?

Does that mean that the non-linearity is significant if p < 0.05 cause I have an edf of bigger than 2?

model 1 smooth terms edf p-value
s(week):typeFruits 3.0000 0.0895
s(week):typeVege 3.0000 0.0008
```

What does the p-values besides the edf means in generalized additive model (GAM) mean?

Does that mean that the non-linearity is significant if p < 0.05 cause I have an edf of bigger than 2? Package used is mgcv

Family: Beta regression(1.35) 
Link function: logit 

Formula:
outcome ~ s(week, k = 4, fx = TRUE, by = food) + food
Parametric coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  0.72943    0.08153   8.947   <2e-16 ***
typeFruits  -1.56222    0.10075 -15.507   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Approximate significance of smooth terms:
                      edf Ref.df Chi.sq  p-value    
s(week):typeFruits   3      3  6.504 0.089509 .  
s(week):typeVege     3      3 16.802 0.000776 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

R-sq.(adj) =  0.233   Deviance explained = 38.2%
-REML = -312.88  Scale est. = 1         n = 612
```