The Finnish Coat of Arms is defined in the law as:
"...on a red field, a crowned lion, who holds a raised sword on the armored right arm, and tramples a scimitar. The lion with the crown and armaments, the hilts of weapons and and the armor joints are golden, and the weapon blades and armor are of silver. On the field, there are nine silver roses."
(The law also mentions that like the flag, it should not, under any circumstance, be altered to be significantly different from the description...)
This coat of arms is used in various nationally important items, for example, on the coins (currently it can be seen in every Finnish eurocent), stamps and seals. It also appears in the state flag (not the "normal" flags, though). The lion is often just referred to as "Suomen Leijona" ("The Lion of Finland"); it's not a great wonder the national hockey team is also named after this beast.
The coat of arms goes back to year 1556. King of Sweden, Gustav I, made his son John the duke of Finland. John himself probably never actually used the coat of arms, though. Later, around 1581, it was slightly changed. The lion is derived from coat of arms of Folkung family, and the swords are taken from Karelian coat of arms. The trampled oriental sword is a Russian one, reflecting the political climate at the time. The amount of roses has varied over time, but it is not a reference to nine historical provinces of Finland or anything like that - they're just decorative.
The coat of arms was written in law in 1978.