Upstream is a term used to describe something that is located opposite the direction of transcription; that is, in a 3' → 5' direction along a strand of DNA or RNA.
The 3' (pronounced three prime) end of a genetic molecule, whether it be DNA or RNA, is the one with a hydroxyl group (OH) hanging off the end of the pentose sugar (ribose or deoxyribose), or more specifically from the sugar's 3' carbon atom. If we continue with the river analogy that upstream or downstream uses, the 3' end would be in the direction the river flows in, ultimately ending at the river's mouth.
The 5' (five prime) end is the one with a loose phosphate group hanging off the end of the sugar's 5' carbon. In the river analogy, this would be the source.
It's actually much clearer with a picture.
5' ATTCGTCCGATTAGCGTA 3'