Accordions are "free reed" instruments.
Sound is made by a reed [thin metal ribbon] that is held at one end and free at the other, like a ruler on the edge of a table top. The reed is fitted inside a holder plate, air is drawn through the hole in the holder, the reed vibrates, voila.
There are many many different kinds.
The first free-reed instrument was the Chinese sheng (笙 sheng1), which is mouth-blown. It is thought that a traveler to China in the 1800s brought this idea back to Europe.
The first modern accordion was a 10-button accordion, invented in Germany around 1830 or so, which had the 7 notes of a major scale, and consequently only played in one key [and its related keys]. These accordions are still played today and are called many things, Cajun accordions, melodeons, one-row, diatonic, on and on.
Eventually the piano accordion developed. Familiar to everyone who has ever seen Lawrence Welk, the right hand is laid out like a piano keyboard, so a piano player could play it. The left hand plays in a forest of up to 120 buttons which play bass notes and various chords.
Another type is the chromatic accordion. Usually these have buttons instead of piano keys, but they have all 12 notes of the western scale. Also their keyboards are laid out so that playing a tune has the same fingering in any key [unlike the piano accordion].
Many folk cultures have their own flavor of the accordion, including the Russian bayan, Alpine helikon instruments, North Mexican conjunto accordion, Louisiana Cajun accordion, Irish 2 row b-c type instruments, etc. These can have either a unique note layout, a different sound, or all of the above.
Concertinas are a smaller free reed instrument, but another subject altogether.