early 15c., "act of looking into the distance, condition of facing something else or a certain direction," from Latin prospectus "distant view, look out; sight, faculty of sight," noun use of past participle of prospicere "look out on, look forward," from pro "forward" (see pro-) + specere "look at" (from PIE root *spek- "to observe").
The meaning "extensive view of the landscape, view of things within the reach of the eye" is from 1530s; transferred sense of "mental view or survey" is from 1620s. The meaning "that which is presented to the eye, scene" is from 1630s.
The sense of "person or thing considered promising" is from 1922, from the earlier sense of "expectation, ground of expectation," especially of advantage (1660s) on the notion of "looking forward," hence "anticipation." Hence prospects "things looked forward to." The meaning "a wide, long, straight street or avenue" is by 1866, in a Russian context, and thus often spelled prospekt.