Present Indicative: Contract Verbs

Why contract? Because, if the stem ends in α, ε or ο, for reasons of fluency of speech, that stem α, ε or ο combines with the ending. In Attic Greek anyway.
Look at English: We say things like "doesn't, won't, he's gone, they've left, the're not here". Why? Because it's easier - for us! That's elision, the Greeks do that too. But they found out that for them, contracting action verbs was also easier. For them!
 
 
  lives, is living, is dwelling 
  
οἰκέ ω    becomes  οἰκ ῶ 
οἰκέ εις    becomes  οἰκ εῖς 
οἰκέ ει    becomes  οἰκ εῖ 
οἰκέ ομεν    becomes  οἰκ οῦμεν 
οἰκέ ετε    becomes  οἰκ εῖτε 
οἰκέ ουσιν    becomes  οἰκ οῦσιν 
 
 
 Note 
 
All the endings are regular, only the stem has changed: it has lost its end vowel, ε in this case. And that vowel has combined with the regular endings, lenghtening them. But this ε was an accented έ and the accent has moved with it, changing to a circumflex to let us know that it really is 2 sounds fused into one.
 
Contraction Rules
unaccented accented
  ε + ω      becomes     ω       έ + ω      becomes     ῶ    
  ε + ει      becomes     ει       έ + ει      becomes     εῖ    
  ε + ε      becomes     ει       έ + ε      becomes     εῖ    
  ε + ο      becomes     ου       έ + ο      becomes     οῦ    
  ε + ου      becomes     ου       έ + ου      becomes     οῦ