Does turmeric have a definitive taste?
Turmeric does have its own flavour, even dried.  However it's commonly used with other, stronger, spices.  This means that it adds a bit of depth to the flavour but in a subtle way.

The flavour of turmeric also cooks out to some extent (as does ginger, to which it's related) so adding it towards the end of cooking retains more flavour.  For a highly-coloured dish I make (a mild curry using Quorn or chicken with a yoghurt- and almond-based sauce) I add some early, and some more after the yoghurt.  Without the latter, the flavour isn't as good; without the former the colour isn't as good.

If you want to get an idea of the taste of turmeric on its own, try steeping some in a little vodka, straining, and sipping.  I did this recently for other reasons and the taste is quite pleasant, if unexpected in a drink.