Trophy pushing is a strategy in Clash of Clans where you attack whenever you can and don't care much about loot. Most people that trophy push are in Town Hall seven or above so that the can get into Crystal, Master and Champion League. Most commonly, trophy pushers take the first base they find, that they have a chance at beating. but in some cases, they will only attack if the trophies are high enough if you win.
Trophy pushers usually don't care if they get a three star or not they just care if they win.
Some good trophy pushing tactics are, DragHogs for TH7 with 2 Heal Spells and 1 Rage. For TH8 you could use P.E.K.WiValk which is P.E.K.K.A's, Wizards and Valkyries with a Poison Spell, 2 Rage Spells and a Heal and for TH9 you could do WiGoValk which is Witches, Golems and Valkyries with whatever spells you like.
With all of these attack strategies you should also use a Hero walk ;)