You might just want to look "downstream" and "upstream" up in a dictionary. These are generic English terms. But because I'm feeling nice this morning:

Imagine a river. Rivers flow in a single direction and if you placed something (that floats) in a river it would float with the current, passing by points along the coast in a set order (after all, it's not going to float against the current). If you were standing on the shore and the object were floating toward you, then it'd be upstream of you. After it passed you, it'd be downstream of you. In English, we generalize these terms to apply to any set of processes with a (roughly) linear ordering. So when you first get sequencing data, you'll probably perform some quality control steps and then alignment or assembly. These are the upstream-most steps. Once, that's done, the downstream steps (variant calling, counting alignments per gene in RNAseq, calling ChIP peaks, etc.) are performed, which generally is when the data starts getting more interesting.