Day in astronomy
In astronomy, the word day has as many as three specific meanings:
A solar day is the time that a celestial body requires to present the same face toward the sun, or toward its own star in the case of an extrasolar planet. On Earth the solar day is 24 hours, or 86,400 SI seconds.
A synodic day is the time that a celestial body requires to present the same face toward its own particular primary. For planets and dwarf planets in orbit around the sun, the synodic day and the solar day are the same. For moons, the synodic day is the day between "rises" of a moon's primary in that moon's sky.
A celestial body in tidal lock with its primary does not have a synodic day.
Day in the Bible
According to the Biblical book of Genesis God created the heavens and the earth in six days, and rested on the seventh. It should be noted that a day within the Bible is not always a 24 hour period. Sometimes, to God, a day is as a thousand years. 
However, the Bible defines the word day (Hebrew yowm) most clearly by the context of its use in Genesis 1 . In Genesis 1, the word day appears six times, preceded by the phrase "evening and morning," clearly indicating a solar day.
Outside of Genesis, the word day appears more than four hundred times, and never means anything other than an ordinary day.
The day-age controversy
Progressive creationism, in an attempt to compromise Scripture with geological uniformitarianism and evolution, states that each of the "days" in Genesis 1 were actually great ages of the earth. This interpretation fails for a number of reasons. The most salient reason is that Genesis tells us that plants were created on Day 3, while the sun and moon were created on Day 4. While plants might survive one solar day without light, they would not survive for millions of years without light. Nor does progressive creationism say where the light of the first "day" of Genesis 1 came from. (In addition, most uniformitarians insist that the sun existed before the earth, and in fact date the sun primarily by adding a few hundreds of thousands of years to their value for the age of the earth.)