Abarim Publications' online Biblical Greek Dictionary
The preposition προς (pros) means toward (hence words like prosody and proselyte). It should be distinguished from προ (pro), which means first or in front of (hence words like proton and prophet).
Our word may describe a motion coming or going toward a place or point in time (or opinion or degree of learning, etcetera), or an item's proximity to another thing, place or point in time. It may describe the length of time a situation endures (say, coming on to a year), and even the relative direction that one object (or opinion) has relative to another one.
Especially in later texts, our word is used with such an emphasis on location and little on direction that it assumes a degree of similarity with the preposition παρα (para).
Our word is incorporated in a long list of compound words, in which it expresses direction towards or situation near, but also accession and thus addition and thus repetition, which brings it close to the meaning of the prefix επι (epi).