Summer Solstice

The Summer solstice is the summer time meeting between the gods of Olympus. The summer solstice is the longest day of the year, wheras the winter solstice is the exact opposite, in which it is the shortest day of the year and is the time when the gods' powers are weakest. It occurs every year on June 21st. It is also the day when the gods' magic/power is strongest.

The Lightning Thief
After Percy, the son of Poseidon, survives the hellhound's attack in The Lightning Thief, Poseidon claims him. This causes discord among the gods of Olympus, as this is proof that Poseidon had not honored the pact he had made with his two brothers.

After Zeus' lightning bolt is discovered to be missing, Zeus suspects Poseidon used Percy to steal it, and demands he returns it by the Summer solstice, and Poseidon in turn wants an apology for being suspected by that same date.

In The Lightning Thief, a quest is given to Poseidon's son Percy, to find the missing lightning bolt and return it in time in order to stop a war amongst the gods. If he failed, it would be the Trojan War all over again, except on a much larger scale. Nature would be at war with itself, and it would be many years of battle until the winner came to victory, and nothing could be sure about what the world would be like then.

Percy Jackson succeeds in his quest as he recovers Zeus' lightning bolt by the Summer solstice, reveals the true thief to Zeus (the actual thief who stole the lightning bolt was Luke Castellan, son of Hermes), and Poseidon gets to meet his son formally at the Summer solstice. Poseidon feels very sorry for Percy, because being a hero means a tragic end most of the time. Percy tells his father he isn't sorry for being who he is, and Poseidon tells him that he is a true son of the sea god.

The Lost Hero
After Leo announces that he must build the Argo II, Chiron mentions that they must sail by the summer solstice (which gives them six months), because that's when the gods' powers are strongest and summer winds will be the easiest to navigate.

The Son of Neptune
While on the quest to free Thanatos, Percy has a dream of Piper, Jason, and Leo, as Leo fixes the Argo II. Piper mentions that they were supposed to leave on that day, since it was the solstice. Since the events of The Son of Neptune happened approximately around the 20th-24th June, it's most likely Piper was talking about the summer solstice.