The topic above looks a bit complicated, but it's actually quite easy. "Colloquial" means "casual" as opposed to "formal," and a "contraction" is just the shortening of words. So let's talk about some of the ways that words are shortened in casual speech in American English. 

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In American English, the colloquial contractions you'll hear most often are:

"kinda" [kind of], "wanna" [want to], and "gonna" [going to].

Captions 8-9, English with Annette O'Neil - Colloquial Contractions

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These words are just casually spoken contractions of "kind of," "want to," and "going to."

I just kinda stay away from all that. It's not part of my life.

Caption 77, Ask Jimmy Carter - Interview with Cameron Diaz

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You do wanna keep your resume to one page.

Caption 4, Job Hunting - 4 Resume Do's & Don'ts

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You also do wanna highlight the results, the experiences.

Caption 16, Job Hunting - 4 Resume Do's & Don'ts

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What are you gonna [going to] do with it when you grow up?

Caption 8, A Charlie Brown Christmas - Snowflakes

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You definitely do not want to use these kinds of informal words in formal writing, for instance when applying for a job! 

There's another similar contraction that you will commonly hear among native speakers of American English: 

I'll talk to ya later, Mick. I gotta go.

Caption 32, A Mickey Mouse Cartoon - Goofy's Grandma

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I mean, you show up and your hair's gotta be in place and the lipstick has to be right.

Caption 43, Nicole Kidman - Batman Forever

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The conjunction "gotta" derives from "got to" or "have got to," in the sense of "have to" or "must". A more formal version of the sentences above would be "I have to go" or "I must go," and "Your hair has to be in place" or "Your hair must be in place."

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Further Learning
Watch this video on Yabla English to learn about more contractions, and search the videos on Yabla English for more real world examples of these colloquial contractions used in a real world context.