GONNA= (coll.) Be going to.

WATCH ME BURN= The sensory verbs (see, watch, sound, taste, feel hear) can be followed by infinitive without to (as in this example) or by -ing, but there's a little difference in meaning:
+ INF WITHOUT TO (you perceive the complete action, from beginning to end)
- I saw him cross the street (I saw all the action)
- I heard him sing a song (I heard all his song)
+ -ING (you perceive that person/animal/thing in the middle of the action)
- I saw him crossing the street (when I looked, he was crossing the street, but I didn't see the beginning of the action and maybe I didn't see the end of the action either)
- I heard him singing a song (I just heard a fragment of the song)

I HIT THE FLOOR= (coll.) If you hit a place, you go there. The floor here refers to the dance floor.

'CAUSE= (coll.) Because (also spelled COZ in BrE and CUZ in AmE)

THAT'S MY PLANS= It should be "those are my plans" or "that's my plan". The author was probably thinking of "my plans" as a package, as one thing, so he uses a singular verb (informal English can be much more flexible, but standard English would consider this a mistake).

BRANDS= A trademark or distinctive name identifying a product or a manufacturer. Famous brands in clothing are: Levis, G-Star, Lacoste...

FOR BOTH MY HANDS= For my two hands.

IT GOES ON= It continues. The form "it goes on and on and on" is emphatic, so it means "it never stops".

I THROW MY HANDS UP IN THE AIR= I put my arms high up.

AYO= It's a merging of "Hey, Yo!", two colloquial greetings put together. It is mainly used when addressing an individual in any given situation to get his or her attention.

GOTTA LET GO= I have to relax.

MY CREW= (informal) My friends.

CLUB= Disco.

I'MA= (coll.) I'm going to.

LIKE= The word "like" may be a verb or a preposition, but here it is used as a conjunction, which happens a lot in informal English, especially in America. -Preposition: You are beautiful like the moon
-Conjunction: You look tired like you have been working all day
The standard construction would be using the conjunction "AS IF"
- You look tired as if you had been working all day
In the song we can see several constructions with LIKE as a connector:
- I'm gonna take it all like I'm gonna be the last one standing
- Higher over all like I'm gonna be the last one landing
- We gon' light it up like it's dynamite
All these sentences would be in standard English AS IF + past:
- We gon' light it up like it's dynamite = We're going to light it up as if it were dynamite.

YOU TURN ME ON= You excite me, you impress me.

RUN AWAY= Escape, flee.

TAKE A CHANCE= Risk, this is your opportunity.

DON'T EVER LOOK BACK= Never have regrets (don't look back to the past)

GON'= (coll.) gonna = be going to
- We gon' rock this club = We're going to rock this disco (we're going to party wilder than anyone else)
- We gon' go all night = We're going to be dancing all night long
- We gon' light it up = We're going to bring fun to it

ROCK= (coll.) If you rock a place you agitate it, you cause a commotion there, in this case because you party and dance so much and good that everybody gets overexcited about you.

LIGHT IT UP= If you light something up, you put fire to it so it starts burning. The song says "we gon' light it up like it's dynamite", it means: we're going to make it burn just as you make dynamite burn and it explodes". To make the club explode means to start a wild party, to have great fun.