We're in Latin territory now, folks. Locus amoenus means a "pleasant place" and it's a common literary space where people chill out. Typically, it's a garden, somewhere with lots of nature going on, often enclosed or literally separated from the outside world.
This image makes a small, but important, appearance in the very beginning of Utopia, when the three men head back to Thomas More's house to have their talk:
"After greeting one another and exchanging the usual civilities of strangers upon their first meeting, we all went to my house. There in the garden we sat down on a bench covered with grassy turf to talk together." (1.11)
More than just a lovely place to have a conversation—although gardens are totally that—the retreat to a garden for a specifically philosophical conversation was a typical move in philosophical dialogues. This matters because even though Utopia is a story about travel and a new world, this moment in the garden is signaling that it is also meant to be read as a work of serious, philosophical importance.
The locus amoenus can also refer to the Garden of Eden, that Biblical paradise that Adam and Eve were kicked out of for eating that darn fruit of knowledge. It makes sense that we'd be thinking about that image in a book that describes, for Hythloday at least, the "paradise" of Utopia in contrast to the Fallen (hint: sin, sin, sin) world of Europe.
In fact, the idea of a locus amoenus and the idea of a utopia have some not-so-subtle similarities: they're both isolated from the outside world, seem to be very peaceful, and, no, it's no coincidence that those Utopians love their gardening. These similarities suggest that we can read the whole island of Utopia as one big version of the locus amoenus. As the Garden of Eden connection makes clear, the locus amoenus, like a utopia, is a place that seems to be perfect but is actually problematic. Both concepts, then, are also reminding us that perfection itself is a problematic concept.
Fun Fact: Utopia was written during the time of New World discoveries (more on that in "New World Discovery") and some people actually believed that if Europeans sailed around the world enough, they would actually find the Garden of Eden (as of yet: no luck). So travel, new beginnings, imaginary worlds, sin, gardens... yep, they're all actually brought together in the image of the locus amoenus.