During WW2, Estonia was annexed by the Soviet Union under the Molotov-Ribbintrop pact, which carved up eastern Europe between Stalin and Hitler. Hitler later reneged, and invaded the area assigned to Stalin, taking over the Baltic States (Estonia, Lativa and Lithuania). The Russians later retook Eastern Europe, and re-occupied the Baltics. They didn't leave until the early 90s. Many Russians resettled in Estonia during the occupation, mostly taking lower level jobs - the standard of living has always been better there than in Russia. They now form about 1/3 of the population.
In central Tallinn (the capital of Estonia) the Soviets set up a war memorial to the Soviet 'liberators' who died driving out the Nazis. To the Estonians, however, the 'Bronze Soldier' just commemorated a second occupation - one that went on for nearly 50 years. In 2007 the now-independent Estonian government decided to move the statue to a Soviet military cemetary in the edge of town. The ethnic Russian Estonians objected, as did Russia, and Putin personally called it a desecration. There were riots, and even one death in Tallinn.
The statue was moved, and it was at this point that the cyberattack was launched.
The kid accused is a Russian Estonian. It remains unclear who ordered the attack - Putin's gang could easily have provoked otherwise uninvolved hackers in the Russian diaspora to act.
The attack certainly served Russia's interests at the time, punishing a tiny, resented upstart for daring to act with sovereignty. That there is plausible deniability doesnt clear Putin and his ex-KGB cronies.