Light-Year
A light-year is the distance light travels in one year, about 9.46 trillion kilometers, used to measure distances between stars and galaxies.
Formula
1\ \text{ly} \approx 9.46 \times 10^{12}\ \text{km}
Definition
A light-year is a measure of distance, not time: it is how far light travels in one year, about $9.5$ trillion kilometers, and astronomers use it because space is too big for kilometers to be useful. Light moves at about $300{,}000\ \text{km/s}$, so one light-year is about $9.46 \times 10^{12}\ \text{km}$, the standard unit for distances to stars and galaxies, while the astronomical unit serves inside the solar system. Formally it is the distance light travels in vacuum in one Julian year of $365.25$ days, $299{,}792.458\ \text{km/s} \times 3.156 \times 10^7\ \text{s} \approx 9.461 \times 10^{12}\ \text{km}$, or about $63{,}241\ \text{AU}$. Professional astronomers more often use the parsec, defined by parallax, with $1\ \text{pc} \approx 3.26\ \text{ly}$, and at cosmological distances the light-travel distance differs from the present proper distance because space expands during the trip.
Example
Proxima Centauri, the nearest star after the Sun, is about $4.2$ light-years away, so its light left more than four years before reaching your eyes tonight. The Milky Way is about $100{,}000$ light-years across, and the Andromeda Galaxy at $2.5$ million light-years is seen as it was before modern humans existed. Proxima's parallax of about $0.77$ arcseconds gives $1/0.77 \approx 1.30\ \text{pc}$, or $4.24\ \text{ly}$, and a probe traveling at $60{,}000\ \text{km/h}$ would need over $75{,}000$ years to reach it.
Key Insight
Because light takes time to travel, looking at distant objects means looking into the past: if a star $500$ light-years away exploded today, nobody on Earth would know for $500$ years. Light-minutes and light-hours are handy too; the Sun is about $8$ light-minutes away and Neptune about $4$ light-hours, which shows how tiny the solar system is next to a single light-year. The finite speed of light is what bounds the observable universe: not a wall, but the $13.8$ billion years light has had to travel.