The local bus service can take people to nearby towns and villages. The number 352 goes to Chelmsford, and the number 70 goes to Colchester. They both stop outside the public library rather than, as one might reasonably expect, the local bus depot and are your best bet if you want to go somewhere decent via bus.
Braintree's train line is a spur off of the national service, and all trains leaving will be heading for London, The freqency of these trains is once every hour. Trains take about 45 mins to reach London stopping at various stops along the way.