You can cast a spell as if it were a higher level. For example normally a sorcerer can cast light as a 0 level spell. If they were in an area of darkness the light spell wouldn't work. You could Heighten the spell and cast it using a 3rd level spell slot to overcome the darkness spell. Heighten does increase the duration, saving throw etc but it's still the same spell and you have to be able to expend the higher level spell slot.
Heighten Spell increases the actual level of the spell prepared with it. Normally, it doesn't matter if your charm person spell has Persistent, Bouncing, Extend, and Threnodic metamagic feats applied to it and you've chosen to use a 9th level spell slot for it: said incantation still has a save DC based on being a 1st level spell, and this mightily-modified charm can't work against a target inside a globe of invulnerability. When you add Heighten Spell to it, that spell can now act as if it were a 9th level spell for save DCs and interactions with other spell effects, like that globe I just mentioned. It has no effect on duration, range, or any other effects, as those are all based on caster level, not spell level. Heighten Spell lets you adjust the functional level of the spell modified by it.
As Lathiira said.
Heighten is mostly a way to get better DCs with low level spells by casting them with higher level slots.
Example: an oracle 16 with 8th spell slots can modify the 1st level spell Sanctuary up to 8th, thereby increasing the save. It does nothing else to the spell's stats.
The oracle could use a command spell and modify it with persistent (+2), which would cost a 3rd level spell slot. He could also tack on Heighten to use any slot between 4th and 8th level to increase the DC. This does nothing to the effect of command itself. If he would use a 6th level slot, he would have dedicated 3 levels (3rd level is already spoken for by persistent) to Heighten, making it a 4th level spell, able to bypass a Minor Globe, too.
Heighten is a toy for high level casters, because you don't have the higher slots at low levels. And then they often have spells making Heighten obsolete. Someone with Greater Command (5th) would hardly use the feat on the 1st level spell.
I just need to know exactly how the Metamagic Feat Heighten Spell works. Do I cast a first level spell as if it were a 2nd level? Such as allowing a 1st level Transmutation spell to take the form of a second, allowing a Level 1 Sorceror to cast a 2nd level spell he doesnt know? Or would it simply increase the duration of a spell that said Duration: 1 min./level?
You cast a 1. level spell as if it were a 2. level spell. That includes using a 2. level spell slot (requiring you to be at least a 4th level sorcerer), using the save DC of a 2. level spell, and counting for all purposes like a 2. level spell. But the spell is still, for example, Animate Rope (a 1. level spell); it doesn't become Levitate (a 2. level spell).
Duration: 1 min/level means one minute per caster level, not spell level. You might want to read the magic chapter, the one that precedes the spell chapter.