Considering the political and historical context in which the term glasnost I feel it deserves more than a simple translation to english. So for your edification and wonderment I would like to now provide a complex translation, with a little bit of etymology thrown in to spice things up.
Glasnost': this word is made up of two separate meaningful parts: glasn- and ost'. Glasn- is the word stem, most commonly seen in the adjective glasnii, meaning public. The suffix -ost' is a commonly used suffix to change an adjective into a noun with the meaning of "being in the state of" the adjective. For example the word molodost', meaning "youth" (or the state of being young), is a common word formed from the adjective molodoi, "young". One of my hoziaka's favorite toasts is za molodost', or "to youth."
So glasnost', from glasnii, means the state of being public, which we translate as "openness" because "publicness" sounds a bit odd in English.