Minnesota's current biennial legislative structure is known as a flexible biennial session. The House Research publication Regular Sessions of the Minnesota Legislature explains the structure of Minnesota Legislative Sessions, and flexible biennial sessions, in greater detail: "Each legislature may schedule its regular session meetings as it pleases, as long as it does not exceed 120 legislative days or meet outside of the January-to-May period. The session is biennial because each legislature is allowed, though not required, to meet in both years of the biennium: when it closes the regular session in the first year, the legislature can choose to adjourn either sine die or to a date it specifies in the following year."
Minnesota hasn't always had a flexible session. The flexible biennial session has been an option for the Legislature since 1973, the result of a 1972 constitutional amendment. That amendment did not require annual sessions of the Legislature. Rather, it just allowed for them to happen. The Minnesota Legislature has met in session every year since 1973, taking advantage of the flexible session option.
The first year of the biennium begins in January of the odd-numbered year and typically lasts until the constitutional adjournment deadline in May. The second year of the biennium has a flexible start date and is usually shorter than the first year. Typically, the Legislature convenes in February of the even-numbered year and is in session through the constitutional adjournment deadline in May.
For historical information on Minnesota legislative sessions, see Sessions of the Minnesota State Legislature and the Minnesota Territorial Legislature and Special Sessions of the Minnesota Legislature and the Minnesota Territorial Legislature.
You may also be interested in other FAQs about sessions.