The first Finnish census was organized in the year 1749, when Finland was still a part of Sweden. This census found that the Finnish population was 410 400 people in size. 

When the living conditions began to grow better at the turn of the 19th and 20th centuries, the mortality rate became smaller while the birth rate remained high. People continued to have a lot of children, but more of these children began to actually live to maturity, as there was more food available and the health care and hygiene standards were better. This lead to rapid population growth. 

By the 1930s, the birth rate had began to decrease, and the average family had approximately two children. During World War II, the birth rate dropped drastically. However, once the war was over, Finland experienced a "baby boom" where the birth rate skyrocketed. The post-war generation is often called the "baby boomers". After this sudden rise, the birth rate dropped back to its old, low state. 

Nowadays, the Finnish birth and death rates remain at a similarly low level. Because of this, the Finnish population experiences almost no natural growth. As living standards have increased, Finns have become more educated. Because of this, people often start families later in life than their parents did. The average age of women giving birth for the first time has increased. Because of this, women do not have a lot of time to have give birth to as many children.

If immigration is not increased, the Finnish population will probably begin to decrease during the next few decades. As the Finnish population grows older and the number of working-age people decreases, the nation can end up in a situation where it cannot provide enough services for its aging population.

Demographics of Finland (Wikipedia)