Alright, so here's what's happening. Dnmt3a is an enzyme that transfers methyl groups to DNA. What they're doing here is assaying its activity under three different conditions with two different DNA substrates because they're interested in how fiber formation affects Dnmt3a activity. In the first condition, they're pre-incubating with biotinylated substrate, which basically means it's a DNA with biotin attached to it. The biotin is not relevant for the reaction. All it does is it binds to avidin very strongly so that when you quench the reaction, you can pull down the product with avidin and measure how much you have by radiation counting (not particularly relevant here - that's just how they get their methyl transfer rate).
So look at the graph. The only ones that are significantly different are Conditions 1 and 2 with 509mers so you should focus on that and why they're different. Alright, so how does Dnmt3a work? Presumably, from the information given, it binds to the DNA, maybe forming a fiber, and then transfers methyl groups to the DNA. So apparently, in Condition 1, it's doing it really really fast and it's doing it a bit slow in Condition 2. What's happening?
Well, condition 1 is when you're pre-incubating the enzyme with the DNA substrate. So the key thing is to notice that the incubation time is purely for the enzyme to get attached to the DNA. So when you incubate with the biotinylated substrate, the enzyme is binding to the DNA and then converting the substrate into the product which you can then pull down later using the avidin. So it's doing it very very fast relative to no pre-incubating (condition 3). That tells you that binding of the enzyme to the DNA accelerates the reaction a lot.
Okay, so why does it slow down in Condition 2? Well, then you're pre-incubating with non-biotinylated substrate, which cannot be pulled down with avidin. So in effect, your product is invisible. The only way this can happen is if the enzyme goes onto the non-biotinylated DNA during the pre-incubation time and binds very tightly so that when you introduce biotinylated DNA, it's still bound and can't get off it. Otherwise, if it didn't bind tightly, it would just come off, go onto the biotinylated DNA, and you would see an increase in methylation rate to a point somewhere between Conditions 1 and 3.
So another way of saying it binds tighter is that it's more stable.