What was so singular in the shapes, habits and countenances of the people of Laputa?

The Lilliputians were certainly unique. I'm going to give you a quote from the text that summarizes what you are asking:

Their heads were all reclined either to the right or the left; one of their eyes turned inward, and the other directly up to the zenith. Their outward garments were adorned with the figures of suns, moons, and stars, interwoven with those of fiddles, flutes, harps, trumpets, guitars, harpsichords, and many other instruments of music, unknown to us in Europe. I observed here and there many in the habit of servants, with a blown bladder fastened like a flail to the end of a short stick, which they carried in their hands. In each bladder was a small quantity of dried pease, or little pebbles (as I was afterwards informed). With these bladders they now and then flapped the mouths and ears of those who stood near them, of which practice I could not then conceive the meaning; it seems the minds of these people are so taken up with intense speculations, that they neither can speak, nor attend to the discourses of others, without being roused by some external taction upon the organs of speech and hearing; for which reason those persons who are able to afford it always keep a flapper (the original is climenole) in their family, as one of their domestics, nor ever walk abroad or make visits without him. And the business of this officer is, when two or more persons are in company, gently to strike with his bladder the mouth of him who is to speak, and the right ear of him or them to whom the speaker addresses himself. This flapper is likewise employed diligently to attend his master in his walks, and upon occasion to give him a soft flap on his eyes, because he is always so wrapped up in cogitation, that he is in manifest danger of falling down every precipice, and bouncing his head against every post, and in the streets, of jostling others, or being jostled himself into the kennel."