Just like prepositions in English, prefixes in Russian have certain meanings, so the logic will be similar in other verbs as well.
"у-" most often means 'away' (убежать, уехать, улететь, уйти - to run away, to go away, to fly away, to walk away, etc.)
"про-" ofter means 'through' - both in the meaning of direction and completeness of the action (пройти, прочитать, проехать - to go through, to read through, to ride through, etc.)
"вы-" is similar to 'out' (выйти, выбраться, выглянуть - go out, get out, look out of smth, etc.)