Can someone please explain the following jargon to a layman
So I can definitely explain what "inhibits" means and what that implies, but I think the answer as to what apigenin is actually doing to testosterone levels is somewhat complicated. I wasn't able to find a study looking at steroid levels in vivo following apigenin administration, so this is based solely on a quick look through the biochemistry and cells biology available. 

17β-HSD is an enzyme that catalyzes a reaction (meaning it makes the chemical reaction happen more quickly than it would by itself) that converts androstenedione to testosterone. If it is inhibited, that means that the enzyme is no longer able to catalyze the reaction. Therefore, inhibition of this enzyme should prevent the synthesis testosterone, and reduce its levels, since less testosterone will be made.

On the other hand, aromatase is an enzyme that converts androgens, namely testosterone and its aforementioned precursor androstenedione, into estrogens. So, one would expect inhibition of this enzyme to lead to increased testosterone levels, as less testosterone and androstenedione would be converted to estrogens, meaning more testosterone and its precursor are left unchanged. 

So, it seems we have some competing actions. Based on the paragraph in your question, apigenin's IC50 for 17β-HSD is 0.3 μM, and its IC50 for aromatase is about 2.9 μM. That means that when the concentration of apigenin is 0.3  μM, the enzyme activity of 17β-HSD is cut in half, but it must be at a concentration of 2.9 μM to do the same to aromatse's activity. So, it is about ten-fold more potent at inhibiting 17β-HSD than aromatase, at least in the assays used above. That would suggest that at concentrations significantly below 2.9 μM, apigenin would inhibit 17β-HSD but not aromatase, resulting in a decrease in testosterone. However, once concentrations became sufficiently high to allow for inhibition of both enzymes, things would get more complicated. Depending on the relative amounts of both enzymes, how much access apigenin was able to get to each, and what the cellular steroid composition was prior to inhibition, you could imagine relative testosterone levels to go either up or down. However, I would be inclined to suspect that testosterone levels would in fact decrease in the long run, since eventually existing testosterone stores would be depleted, and the inhibition of 17β-HSD would prevent the creation of new testosterone. 

However, if we look at the paragraph in the article immediately following the one you quoted, there is a summary of a study done in cells that found that apigenin actually increased testosterone levels by blocking the TBXA2 receptor. This inhibited a signaling cascade that normally decreases testosterone synthesis, so the end result was an increase in steroidogenesis/testosterone production. 

So, I suspect things are actually somewhat complicated and the best way to know would be to test in vivo