It is eaten in a number of ways. It can appear in a savoury context - in Kerala, for example, a typical accompaniment is kadala (chickpea) curry. Perhaps more often it features sweet accompaniments, especially banana, another South Indian staple.
The puttu pictured below was sampled in Malaysia, for breakfast at Susi's Banana Leaf Corner in Petaling Jaya. This particular one was made with atta (Indian whole-wheat flour), hence the brown colour.
It's a simple but tasty combination, and the sort of honest home-style dish that invokes a sense of nostalgia amongst many Indians and Sri Lankans. Puttu on its own doesn't have a great deal of taste (and thus needs its accompaniments) but much of its appeal lies in its delightfully chewy texture.
Aside from the cuisines of Sri Lanka (where it is known as pittu) and South India, puttu has also ingratiated itself into the Malay and Indonesian culinary traditions. The Malay putu piring is disc-shaped rather than cylindrical, and contains a filling of palm sugar. (EatingAsia has a nice post on these.) The Indonesian kue putu also has the palm sugar filling, but retains the cylindrical shape. These are frequently green in colour, from the extract of the pandan leaf.
The shape of puttu suggests that originally it probably would have been steamed inside a hollow stem of bamboo; many peoples through tropical Asia still steam rice and other foods this way. Tamils and Malayalis have been trading in the Indonesian archipelago for over 2000 years, so it's hard to say whether this recipe is an ancient addition to the cuisine of that region, or arrived more recently with large-scale Tamil settlement of Malaysia under the British.
Spicy Susi's Banana Leaf Corner, No.1A, Bangunan SKPPK, Jalan SS 9A/17, Petaling Jaya, Malaysia.