The suffix -ing serves a few different purposes:

1) Construction of a present participle from a verb to describe an action in progress.

2) Construction of a gerund from a verb to serve as a noun in a sentence.

3) Construction of a gerundive form from a verb to serve as an adjective or adverb.

4) Construction of certain kinds of uncountable nouns (there are no hard rules here, only certain words that can be used in this construction)

If you want to think about it intuitively, -ing takes an abstract concept or action and associates it with process, action, or material circumstance.

There used to be more uses of -ing that have fallen out of favor - like forming diminutives and patronymics. In Old English, -ing was used to used to create verbal nouns (like gerunds or present participles above) and also used to create derivatives of masculine nouns.

tl;dr Most native speakers will have a hard time intuitively describing -ing to you. If you speak a Germanic language, you probably already have an intuitive sense of -ing, and if you don't, you'll just have to memorize. Sorry for my language :(