I assume you're talking about the migration waves in the mid- to late 1800s. Counter to expectations, the migration is generally seen to have been a good thing for Norway. Norway was experiencing a population boom, as the period after independence in 1814 was marked by peace and growth. Good midwife practices meant some of the lowest rate of infant mortality rates in Europe, and fishing created a more diverse diet than many other places on the continent.

Nonetheless there were downsides. Only about 4% of land is arable, and while the country was industrialising, it was not at the scale of other European nations. This resulted in a lack of opportunities, which had two consequences:

1. An underclass of farmers, "husmenn", grew in scale. They often did not own the land they farmed, but were different from tenant farmers. Instead of being the subject of a landlord, they were usually related to the farmer who they worked the land for, and lived on a separate house near the property - "husmannsplassen". Some husmenn would do other work on the side, such as moving lumber or work in mines. The proportion of husmenn peaked around 1860-1890, right around the time of the migration waves to the US, but gradually they disappeared in the early 1900s.
2. Migration. Norway was a coastal, ship-building nation with a high literacy rate thanks to early public and religious education. This meant that when there were few opportunities at home, people had easy access to ships to go to the mythologised land of opportunity, America. This was additionally spurred by news articles of generous land opportunities as the US expanded westward, and of Norwegian expats writing letters home of the opportunities they discovered. The letter-writing is one of the factors thought to contribute to the "wave action" of migration, as letters came a while after settling down, leading to more migration. It is worth noting that a large portion of these migrants returned home.

Most historians consider this migration to be a "safety valve" for population growth. As a result of the easy access to the coast and to America, people were able to move before the standard of living became dire. As a result there was no hunger during the population boom. The population was able to keep growing as the country diversified its industries and food output could be increased with new farming techniques and importantly, later, new fertilisation methods. It was during the late 1800s and early 1900s that Norway became an industrial nation in the modern sense, and the country would be able to again accommodate a larger population. It is also worth noting that the population of Norway kept growing when seeing the migration period as a whole, so the migration simply slowed the population growth to manageable levels.

References:

Dyrvik, S. (2017). Året 1814. Oslo: Det Norske Samlaget.

Myhre, J. E. (2018). Norsk historie 1814-1905: å byggje ein stat og skape ein nasjon (2 ed.). Oslo: Det Norske Samlaget.

Opsahl, O. G. M. E., & Sandmo, G. I. P. E. (2015). Norsk historie 1537-1814. Oslo: Universitetsforlaget.