The name comes from alveoli - the sockets of the teeth.
Example
The consonant sounds /t/, /n/ and /d/ are all alveolar consonants.
In the classroom
Alveolar consonants exist in many languages, including Spanish, Italian, French and German. Learners can practise these in minimal pairs such as ‘tent' and ‘dent'.
Further links:
I would like to add /s/, /z/, /l/. Also, /r/ might be considered as alveolar, although some might say it is a post-alveolar sound, when it is articulated as a retroflex.