Origin
The main sequence is the first stage a star experiences after acquiring star status. Before that comes the protostar stage, when gravity causes a cloud of gas and dust, known as a nebula, to swirl and compress over millions of years. It grows denser and hotter at its center. If the core reaches a temperature of about 10 million degrees Kelvin, hydrogen fusion begins occurring, and the main sequence star is born.
Features
The defining quality of a main sequence star is hydrostatic equilibrium. This is a state of perfect balance between compression and expansion, enabling the star to remain essentially unchanged for millions or billions of years.
Gravity continues to attempt to compress the star throughout its existence. This inward pressure causes the gas to exert an outward pressure in return, just as a rubber ball exerts pressure against your hand when you squeeze it. Gas pressure is not a strong enough force to combat gravity, so a protostar can only get smaller and denser. But in the main sequence, hydrogen fusion releases energy, creating not only light and heat but also immense radiation pressure. This combines with the gas pressure already present to form just enough outward force to balance the inward force of gravity. Thus a star maintains hydrostatic equilibrium.
Significance
For life to have arisen on Earth and evolved from single-celled organisms into the various complex species alive today, conditions needed to remain relatively constant for millions of years. This means, on the one hand, that we couldn't exist if our planet weren't orbiting a main sequence star. On the other hand, it means that main sequence stars similar to our Sun, such as Alpha Centauri A, might harbor planets with life on them as well.
Time Frame
The main sequence will last until all the hydrogen has been converted into helium. How long this takes depends on how much mass the star has in the first place. The bigger it is, the stronger its gravity, the hotter its core burns, and the faster it uses up its hydrogen supply. A medium-sized star like our sun will spend 10 billion years in the main sequence stage while a high-mass star can only expect its main sequence to last 20 million years.
Afterwards
The size of the star determines not only the length of the main sequence but also what happens after the main sequence ends. A star the size of our Sun or greater will enter a red giant phase, converting helium into carbon and then carbon into heavier elements. Most such stars eventually run out of fuel and become white dwarfs, but if they are big enough--say, five times the mass of our Sun or greater--they will explode into a supernova.