This is the 14052nd most frequent Swedish word.
övertygande
Convincing.
In this context, 'övertygande' is used as an adjective to describe the quality of the speech as persuading and compelling.
Han höll ett mycket övertygande tal.
He gave a very convincing speech.
Here, 'övertygande' again functions as an adjective, referring to the lack of persuading power of her argument.
Hennes argument var inte särskilt övertygande.
Her argument was not particularly convincing.
In this example, 'övertygande' serves as an adjective describing the impression given by the ideas as being able to persuade or compelling.