We heard about Monteverde on our first trip to Costa Rica while in the Arenal area. They're relatively close to each other so it's common for folks to visit both places on one trip. Monteverde is famous for it's cloud forest and I found the area to be very different from other areas of Costa Rica. A cloud forest is basically a rainforest at a higher elevation. They're cooler and there is usually a layer of fog across the tree canopy. Because of the elevation and the climate the biodiversity in Monteverde is different than other parts of the country and you'll find plants and animals that only exist in Monteverde.
Like Arenal, Monteverde is a very common tourist destination. But unlike Arenal, Monteverde deliberately limits how many people can be in the area at one time. The area never feels too crowded which is nice. This does mean that you should plan your trip ahead of time because the limited hotels will sell out quickly, particulary during peak tourist times. We stayed at the Monteverde Lodge and Gardens and had a lovely time. Their rooms are nice, particularly the ones with balconies, and there is a nice garden to walk around plus an indoor butterfly garden.