Main Sequence
The main sequence is the long, stable stage of a star life when it fuses hydrogen into helium in its core, the stage the Sun is in now.
Definition
The main sequence is the long, steady stage of a star's life when it fuses hydrogen into helium in its core and shines at a stable brightness; most stars, including the Sun, are in this stage. During it the star stays balanced between gravity pulling inward and pressure pushing outward, and on a Hertzsprung-Russell diagram main-sequence stars form a diagonal band from hot, bright blue stars to cool, dim red stars, holding about $90\%$ of all stars. It is fundamentally a mass sequence: luminosity scales roughly as $L \propto M^{3.5}$ for Sun-like stars, so main-sequence lifetime scales as $t \propto M/L \propto M^{-2.5}$. A star leaves the main sequence when core hydrogen runs out, after which the core contracts, the envelope expands, and the star moves to the giant branch.
Example
The Sun has been a main-sequence star for about $4.6$ billion years and will remain one for about $5$ billion more. A star with half the Sun's mass can stay on the main sequence for over $50$ billion years, while a star with $10$ times the Sun's mass lasts only about $20$ million years. Using the scaling law with $t \approx 10^{10}$ years for the Sun, a $4$ solar mass star has $t \approx 10^{10} \times 4^{-2.5} \approx 3 \times 10^8$ years, and a $0.5$ solar mass star has $t \approx 5.7 \times 10^{10}$ years, longer than the current age of the universe.
Key Insight
The main sequence is like the adult stage of a star's life, and because it is the longest stage, most of the stars we see are in it. A main-sequence star's position is set by its mass alone, so its color alone tells you its temperature, brightness, size, and lifespan. Because lifetime falls so steeply with mass, the most massive stars in a cluster leave the main sequence first, and the mass at the turnoff point is the standard way astronomers date star clusters.