Inserting or deleting in a linked list costs O(1) once you hold the right node. You rewire a pointer or two and you are done. Nothing else moves. The rest of the list stays exactly where it sat.
An array behaves differently. To insert or delete in the middle, you must shift every later element over one slot. That shift costs O(n). Only changes at the very end avoid it.
There is a catch worth naming. The linked list is O(1) only after you reach the node. Finding it first still costs O(n) hops. Arrays trade cheap access for expensive reshaping; linked lists do the reverse.
Rewriting in plainer words…
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