Abarim Publications' online Biblical Greek Dictionary
The ubiquitous conjunctive particle ινα (hina) means "that" or "so that", and works pretty much the same as our English word "that".
Sometimes our particle merely ties two halves of a sentence together with very little explanatory force ("I tell you that the phone rings"), sometimes it replaces an infinitive ("I call you to hear you" / "I call you so that I hear you"), but often it introduces an explanatory statement or a statement that conveys purpose or intent: "I'm talking to you so that you get this important information".
Our particle often comes with substantial explanatory or demonstrative momentum: "to the purpose of", "to the end of", "in order to" and as such tends to provoke the optative and subjunctive cases (which express situations wished or hoped for, or those that ought to be). When our particle and the subjunctive appear combined with a statement in the past tense, our particle expresses the certainty of the occurrence of the wished-for thing (Mark 3:14, "so that that they might be with Him", obviously reveals that they surely did and He surely knew they would).
Combined with particles of negation, our conjunction helps to express "so that not" or "lest".