| In phonetics, alveolar refers to sounds made with the tongue on or approaching the alveolar ridge, a small* ridge just behind the upper teeth.
Normally it is the tip (apex) of the tongue that is used, so these are more precisely called apico-alveolar sounds.
The sibilants s and z are alveolar fricatives. The tongue comes close enough to cause friction but does not touch the ridge. A narrow groove down the centre of the tongue causes the sharpness (sibilance) of the sound.
In English, t d n l are also alveolar, as they are in many other languages. But in many languages (French, Spanish, Italian for example) they are dental, that is the tongue points not to the alveolar ridge but a little further forward to the upper teeth themselves.
The difference is slight, but a few languages (notably Australian Aboriginal languages and the Dravidian ones of southern India) use both alveolar and dental sounds, as distinct sounds.
Most Indian languages have a dental t and a retroflex t (and likewise d n l), but not an alveolar one, which is midway between the two. English has neither of those places of articulation, so an Indian speaking English uses one of their own sounds instead, and to them the retroflex sounds seem closer. This is what makes the distinctive t d n l of Indian-accented English.
* 'small' = no, you're right, it's impossible to feel by running your tongue over the area; I'm just taking this one on trust too. | 
