Shir Hashirim has the verse השבעתי אתכם בנות ירושלים, that there was an oath with the daughters of Jerusalem. The Talmud at the end of מסכת כתובות says that this a reference to the "three oaths."
The claim of the Talmud is that there was an agreement between Israel and the nations at the time that Israel went into their lengthy exile. Israel agreed that they would not rebel against the nations that hosted them in Galut. The second oath is that Israel agreed that they would not come to Israel in a mass but a trickle. The third oath was on the part of the nations that they would not oppress Israel "too much." These became known as שלוש שבועות.
In recent years, religious anti-Zionists began quoting the "three oaths" as a justification for not moving to Israel. Mass Aliya constituted a violation of oath number two.
Many Zionist rabbis addressed this question by saying that Israel is no longer obligated to oath number two because the nations violated oath number three by oppressing us too much. This certainly was true with the oppression of the Holocaust as well as other persecutions during our long, bitter exile.
I don't think the three oaths had a practical application. It was more of a Midrashic concept. Therefore, Jews can feel free to make Aliya and need not worry that they are violating any oath.
Yesterday was seven with ספירת העומר.