Bangladeshi food is close to Bengali cuisine on the Indian side of the border but with its own character — more fish, more mustard oil, and a heavy presence of the rivers in everything. The national fish is hilsa (ilish), a large, fatty river fish that Bangladeshis are deeply attached to. Hilsa steamed in mustard paste inside a banana leaf is a dish worth traveling for. During monsoon season, when hilsa runs upriver to spawn, the whole country seems to eat nothing else.
The everyday meal across Bangladesh is rice and dal — plain boiled rice with lentil soup, vegetable curries, and whatever fish or meat is available. Bhorta (mashed vegetables or fish, mixed with mustard oil, green chilli, and onion) is a staple and ranges from mashed potato to dried fish to roasted eggplant. It is unassuming and very good.
For celebrations and special occasions, kacchi biryani is the dish — raw marinated meat layered with fragrant rice and slow-cooked together until everything melts into one. Dhaka's Old Town has restaurants that have been doing this for generations.
Street food is everywhere and excellent. Fuchka (hollow crispy shells filled with spiced potato and tamarind water) are the universal snack. Chotpoti (chickpeas and potato with tamarind and egg) is another. Jhalmuri — puffed rice tossed with mustard oil, onion, green chilli, and chopped vegetables — is sold by cart vendors across the country and is exactly what you want at any time of day.
Bangladesh is a Muslim-majority country, so pork is essentially absent and alcohol is harder to find than in neighboring India — available in upmarket hotels and some restaurants in Dhaka, but not widely. Tea (cha) is universal and good, often served very sweet. In Sylhet tea country, you can drink it straight from the source.