To be dismissive is to be indifferent and a little rude. Being dismissive is a sign of disrespect.
If you're dismissive, you show little consideration for others. If a teacher laughs at a student's earnest answer to a question, that's dismissive. An employer throwing a resume in the trash without reading it? Dismissive. People are dismissive to others they think are beneath them. You can also be dismissive to ideas and suggestions. It's like waving someone or something away and saying, "whatever."