How do I interpret or explain loess plot? I used the following R code:
ggscatter(DF_w, x = "Age", y = "Value", 
          add = "loess", conf.int = TRUE 
          ) 

to get this plot:

However, I don't understand how I can report this in a scientific paper or presentation. I understand the graph suggests a non-linear relationship between X Age and Y Value, where there is some variability until late life when Value declines with increased Age. Is that all there is to it? Is there a way to show this is a significant relationship with loess or do I need to carry out a regular regression / correlation to determine significance?
Any information on interpreting such plots is appreciated.

First off, it's extremely good practice to also show the original data, which puts the loess plot into context. Here, the context is that there is still a lot of variation in the data. For instance, the initial dip looks rather strange and could easily be due to noise - and we only see this because we see the full point cloud, not only the loess line with the confidence band. So this is good.
You ask two questions: one about interpretation, the other about significance. In terms of interpretation, I would discuss the downward slope at the right end, but per above, not really trust the dip in the middle.
In terms of significance, this is harder. You could try to assess whether your loess model explains significantly more variation in the data than a comparison model, like an intercept-only model (a horizontal flat line), or a simple linear regression (a slanted straight line). This is what ANOVA does. The problem is that the standard F test in ANOVA requires knowing how many parameters (degrees of freedom) your model used - and that is notoriously difficult to know in the case of a loess model. Greg Snow's answer to How do I find a p-value of smooth spline / loess regression? gives a few tentative ideas in his penultimate paragraph (though not in terms of variance explained, but his ideas could be adapted to this test statistic).
However, as Greg also notes in his answer, assessing the significance of a spline fit can be done in an ANOVA framework. Given the suspicious behavior of your loess fit, I would suggest that you try a fit using natural or restricted cubic splines with few knots, then test this spline fit against the more parsimonious linear fit.
