What to do with an ANOVA that tells that your GLMM is not significant compared with its nullmodel? I have made a GLMM that gave me one of the variables as significant. However, when I did an ANOVA comparing this model with its nullmodel the result was not significant. This means that my model does not fit my data very well. What can I conclude from here? Does it mean that actually, the model cannot infer anything about the data I collected? Or that there is no effect of that variable in my data?

It means that you cannot say for sure that any variation explained by the model you created can be attributed to anything more than random chance.
That makes it a non-informative model, so inference would be non-sensical.
That having been said, you have one significant variable, you can start there and add other variables one at a time to see if you can build a more robust model. Sometimes having everything in there when some variables are chaotic, robs other variables of their predictive capabilities. But I would have tempered expectation. You may find that you need to seek out new data sources if you need to build a meaningful model!
