The phrase "explain nicely" is correct and usable in written English.
You can use it when you are prompting someone to explain something in a pleasant manner. For example, you could say, "Please explain the task nicely so everyone understands it."
It explains nicely the presence/absence of a formal feature on the light verb.
Their phase-based account explains nicely how and why an argument raises in a successive-cyclic manner to the top position of the sentence.
She was, she explained nicely, sorry to have to leave in such a hurry, but she wanted to get some game for lunch.
The first, reported in Nature Neuroscience and explained nicely in Scientific American, used computer simulations to look at the dynamics of individual proteins in the brain of a sea slug (memory researcher/Nobel Laureate Eric Kandel's organism of choice).
While this simplistic interpretation is tempting, I find it to be misleading for reasons explained nicely in Bowsher et al. 2014 which the authors cite.
And then you get those that... that are very nice and that explain everything nicely to you... that doctor, you don't want to disappoint either.... for that doctor, I will almost go even further... go out to learn, to bring back information and so on, to participate.
[The consultant] will say to you "That class, did you not... do you not remember that class I gave, so and so much time ago", while the [registrars] will explain again nicely.
She called her supervisor, who explained very nicely that there was nothing they could do.
Slate's Matt Yglesias explained this nicely earlier this year:Over the past five years, there's been exactly one fatal crash of a US airplane.
