For morphling - agi = damage, str = health.
When you gain/lose str your current hp is scaled to stay at the same % value. So if you are getting attacked you can morph to strength to increase your health pool, and when you are farming you can morph to agi so you can last hit better.
If you morph full agi then say you have 1000 hp and 10 hp regen, you can regen all your hp in 100 seconds, then morph full strength and have 5000 hp.
That's really all there is to it. People morph full agi, tp to lane/jungle, farm up like crazy, and morph str if they are scared.