This is the 17629th most frequent Russian word.
убедительными
Convincing.
The word 'убедительными' is used to describe the arguments, indicating that they were persuasive.
Ваши доводы были убедительными.
Your arguments were convincing.
Here, 'убедительными' describes the nature of the explanations, portraying them as credible and persuasive in tone.
Его объяснения звучали убедительными, хотя и немного сложными.
His explanations sounded convincing, although slightly complex.
In this case, 'убедительными' characterizes the examples chosen by the teacher as effective in making the students comprehend the subject.