The periodic table wasn’t really invented. Scientists were trying to make sense of all the elements they had found and get them into some order and they found that some reacted the same way so they put them together and it got built up from there.
The periodic table was invented to make sense of behaviour of elements (atomic structure, melting points, reactivity, etc.). It comes about as elements have a periodic behaviour (hence the name of the table). Usually elements are grouped into rows (periods) and columns (groups) depending on atomic and electronic structure with hydrogen in the top left. But other formats can be used depending what information you want to display in a nice way (or to show different patterns – i.e., different periodic behaviour).
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