Lapse rate is the negative of the rate of change in temperature with increasing altitude.
What's up with the "negative" sign? Given that temperature often decreases with increasing altitude, the negative sign allows meteorologists to work with mostly positive lapse rates (it's easier to work with positive numbers).
For example, the standard envirnmental lapse rate is approximately 6.5 degrees Celsius per 1 kilometer, meaning that the temperature decreases 6.5 degrees Celsius over each kilometer of altitude. Again, the standard environmental lapse rate is, by definition of lapse rate, a positive number.
The lapse rate associated with temperature inversions, which are characterized by temperatures increasing with increasing altitude, is a negative number. Yes, it's non-intuitive, so keep your wits about you.
Finally, the lapse rate for an isothermal layer of air, which are characterized by temperatures staying constant with increasing altitude, is zero.