"How high does my fold change have to be for it to actually make a difference?.....I'm wondering if this difference is enough to change the plants' stress response.

Is there a certain value that I can see as a "threshold" or is mere statistical significance enough to confirm the change in the plant?"

You've performed ANOVA and it gave you a certain P-value, mean difference and perhaps 95% CI of the mean difference estimation. All of this is useful information that you will need to contextualize as an expert to make a judgement. Once you are under the alpha for your test (which is almost usually 0.05), then those results are generally good enough (especially after replication) to make a claim. By the way, did you run a post-hoc test or was it just an ANOVA to test if there is a difference between the group means? It helps to also think of log2 changes as fold-change, in your case it is 2^0.63 which is 1.54 fold change. How does that compare to similar studies in your field? The P-value is generally there to guard against Type I errors, making the wrong conclusions about rejecting the null differences given data when you shouldn't have. How is the 95% CI of the mean difference estimation, does it barely exclude 0.0 at the lower bound? If you are close to 0.0 i.e. 0.02 with your lower bound 95% estimation, combined with a p-value edging close to 0.05 i.e 0.049 then you should carefully consider rejecting the null without replication studies because it is possible in the replication/follow up study you get a p-value of 0.051. That doesn't mean your data isn't interesting to consider when you are above the magical alpha value, but you'd have to acknowledge the fact that you don't have enough information in your data to reject the null hypothesis.

There is no cut-off for judging a fold-change (btw: fold-change already is a relative measure; it is superfluous to stress that you your fold-change is relative) being biologically relevant, as this depends on too many factors (what gene, involved in what signally/metabolic processes, in what cells, what is the proportion of relevant cells in the sample, at what time, are the cells synchronized, is the mean change considered or are expression bursts relevant, what compensatory effects can exist, can it be an unspecific side-effect without practical relevance in the cell, it the gene expression change counter-balanced by post-transcriptional or post-translational regulation, etc etc etc). It's your job as expert biologists to make such a judgement.

As Can wrote, the significance test only judges the information from your sample data to compare the sample estimate (b) to a hypothetical population value (h): d = b-h. If the information is considered sufficient, then b can be believed to be "on the correct side" of h, so the test tells us if we may have confidence in the sign of d, or that we can statistically distinguish b from h. This hypothetical value if often zero (h=0, so d = b), it is about interpreting sign of b (here: the sign of the log fold-change calculated from your sample).

Note that the point estimate b is associated with uncertainty. Consider the typical case that h=0. A test tells then that you can have confidence that the sign of b is correct, but not that b itself is correct. It might be that b is rather large and the p-value is small, but a irrelevantly small hypothetical value close to zero would not be statistically distinguishable from this h. So the data may be compatible with irrelevant values of h. If relevance (not statistical significance) is of interest, it's more useful to interpret the confidence interval (CI), which is the range of all possible values of h that would be statistically distinguishable from b (giving low p-values in a test). Only if the limit closest to zero is large enough to be considered relevant, then the information from the sample is sufficient to exclude irrelevantly small values of h and claim a "relevant effect".

But these are all technicalities. How large a relevant effect has to be is an expert judgement and cannot be answered statistically. Very often, biologists don't have much of a clue, so the best one can do to claim that one identified the direction of regulation (and avoid to say that the amount of regulation may not be of any biological relevance).

I agree with Jochen's last paragraph wholeheartedly. While we were discussing basic statistics, I forgot to mention one aspect that is just as relevant as the stats. The gene(s) involved, did you check out their function. If you did some sort of an high-throughput assay, did you do some sort of gene enrichment analysis? What about the genes that were significantly different in expression, does the direction of change (up/down regulaton) make sense? I.e. the genes that were significantly up-regulated were immune genes to start host defense mechanisms, down-regulation of genes that would help starve the fungus/invader of vital resources? Don't get hung up on the numbers as much as the implication of the gene expression changes, does the gene expression changes help with the phenotype explanation? Given enough samples, you can find the smallest of effect sizes that are meaningless but statistically significant.