The eruption led to a lowering of global temperatures - indeed, some scientists believe it led to global cooling. As a direct consequence, crop failures occurred worldwide, with 1816 being known subsequently as 'the year without summer'. The economic, political and social consequences would be widespread.
First-hand accounts of the eruption were given in a biography of the Lieutenant-Governor of Java at the time, Thomas Stamford-Raffles, and relevant portions are below:
An extract of 'a letter from Banyuwangi [East Java]':
At ten, P. M. of the [5th] of April, we heard a noise resembling a cannonade, which lasted, at intervals, till nine o'clock next day; it continued at times loud, at others resembling distant thunder
The first explosions were heard on this Island [Java] in the evening of the 5th of April, they were noticed in every quarter, and continued at intervals until the following day. The noise was, in the first instance, almost universally attributed to distant cannon; so much so, that a detachment of troops were marched from Djocjocarta, in the expectation that a neighbouring post was attacked, and along the coast boats were in two instances dispatched in quest of a supposed ship in distress.
On the following morning, however, a slight fall of ashes removed all doubt as to the cause of the sound; and it is worthy of remark, that as the eruption continued, the sound appeared to be so close, that in each district it seemed near at hand; it was attributed to an eruption from the Marapi, the Gunung Kloot or the Gunung Bromo.
From the 6th, the sun became obscured; and it had every appearance of being enveloped in fog: the weather was sultry, and the atmosphere close and still: the sun seemed shorn of its rays, and the general stillness and pressure of the atmosphere foreboded an earthquake. This lasted several days, the explosions continued occasionally, but less violent, and less frequently than at first. Volcanic ashes also began to fall, but in small quantities; and so slightly as to be hardly perceptible in the western districts.
...Stamford-Raffles again:On the 5th of April, a firing of cannon was heard at Macasar, continuing at intervals all the afternoon, and apparently coming from the southward:—towards sunset the reports seemed to have approached much nearer, and sounded like heavy guns, with occasional slight reports between. Supposing it to be occasioned by pirates, a detachment of troops was embarked on board the Honorable Company's cruizer Benares, and sent in search of them, but after examining the neighbouring Islands, returned to Macasar on the 8th, without having found any cause of the alarm.
The Honourable Company's cruizer Teignmouth was lying at anchor at Ternate [870 miles distant] on the 5th April; between six and eight P.M., several very distinct reports like heavy cannon were heard in the S.W. quarter, which was supposed to be a ship in the offing, in consequence of which the Resident sent a boat round the island to ascertain if it was so. The next morning, however, the boat returned without seeing any vessel in the offing; and the conclusion then drawn was that it might be occasioned by the bursting of some volcanic mountain in that quarter. Ternate Island 5° 0' N. 127° 30'E.