Monsoon in Nepal means rains, not necessarily heavily but pleasantly. Making up for about 60% of the rainfall in the entire year, monsoons are considered to be not a suitable time to explore the treks of Nepal, but is one of the best time for sightseeing in the countryside and the major cities.
Because of it being off-season, the months from June to a majority of August experience less tourism in the area, meaning you can easily get a quieter and more fun time exploring the country. The hills become greener, and with all the dust washed away, the mornings become clearer and thus perfect for sightseeing.
During these times, alongside the beauty of the cities like Kathmandu and Pokhara, great experiences like the Upper Mustang Valley, Dolpa Circuit, Rara Lake, Lumbini, Bardiya and Langtang are great places and treks to explore.