Short answer: Tiki-taka is a possession-based, short-passing style perfected by Pep Guardiola's Barcelona (2008-2012) and Spain.
Tiki-taka emphasizes ultra-short passes, possession, positional play. Barcelona under Pep won 14 trophies in 4 years using it; Spain won Euro 2008, World Cup 2010, Euro 2012. Key practitioners on TenDollarPick: Xavi, Iniesta, Busquets, Messi.