Informal contractions are short forms of other words that people use when speaking casually. They are not exactly slang, but they are a little like slang.
For example, "gonna" is a short form of "going to". If you say "going to" very fast, without carefully pronouncing each word, it can sound like "gonna".
Please remember that these are informal contractions. That means that we do not use them in "correct" speech, and we almost never use them in writing. (If you see them in writing, for example in a comic strip, that is because the written words represent the spoken words or dialogue.) We normally use them only when speaking fast and casually, for example with friends. Some people never use them, even in informal speech.
It is probably true to say that informal contractions are more common in American English.
Also note that, unlike normal contractions, we do not usually use apostrophes (') with informal contractions when written.
On the right are some common informal contractions, with example sentences. Note that the example sentences may be a little artificial because when we use a contraction we may also use other contractions in the same sentence, or even drop some words completely. For example: