If you take the story literally, it's clear from the context that it must be a 24 hour day. For example, night and day is mentioned, where night clearly means darkness. A day really means 1000 years, for example, then the story says it was dark for a large portion of that "day" = 1000 years. Say this is 300 years. Then, there was darkness on the earth for 300 years. All the life God just created would die in the extreme cold that would happen in 300 years of darkness, not to mention plants couldn't live without the light from the sun even if they could survive the cold. And, since the "day" and "night" were caused by the sun shining on that portion of the earth, or not, respectively, God would have had to slow the rotation of the earth considerably for that to be possible. For one, it doesn't make sense that God would later speed it up. For two, I'm sure that would throw off all sorts of things, which would also make life not possible.
If you don't take the story literally, then who cares if that word means day or not because it's just a symbol any way.