The act of countering something means to prevent it from resolving in its entirety. For example, if you play a spell and your opponent plays Counterspell, your spell's effects will never occur (assuming you do not counter his Counterspell).
Lack of a legal target will result in the spell being countered by the rules. If Giant Growth is played on a creature and the opponent plays Putrefy, the original target of Giant Growth would not be legal when it gets to resolve and thus would be countered. The spell or effect will only be countered this way if all of its targets become illegal. If one of the targets for Seeds of Strength becomes illegal, the other targets will still be affected. It is important to realize that however a spell/effect is countered, none of its effects resolve. So, if you play Essence Drain on a creature and that creature dies before it gets to resolve, you won't gain the 3 life because all of its targets are no longer legal.
History in Blue
To date, every color has received some method of countering, but blue receives the most support for it. The classic counter spell is, of course, Counterspell. Over time, Wizards of the Coast came to the conclusion that is just not enough mana for an unconditional counter of any spell. The double-colored mana cast can hinder multicolored decks, but decks using only blue mana could practically consider it just . Its last printed set was Seventh Edition, and Time Spiral would later introduce its modern replacement Cancel.