A long time ago in Sri Lanka the Sangha began to divide itself into two sort of specialties of Monks. There were city Monks who lived in monasteries inside the cities and villages, and they specialized in the study of texts and doing ceremonial functions while the forest Monks lived either in monasteries outside of settlements or they wandered from place to place. Such forest monks specialized in meditation. Over time distinct customs grew up with these two specializations, so for example in Thailand, city Monks (with the exception of the Dhammayut monks) wear bright yellow or orange robes while forest monks always wear brown or ochre colored robes.
Over time these customs evolved further, so for example in Thailand for a long time forest Monks also became specialists in using special chants and other kinds of things that are usually thought of as magic.
In the case of Thailand at least the revival came partly as the result of a reform movement that was founded by King Rama IV when he was a monk that focused on improving the standards of the Vinaya. When this movement grew to include forest monks, this reform movement created a lot of dedicated monks who wanted to live the forest monk lifestyle in a much more meditative role rather than the semi-shamanistic role that the forest monks had slipped into, and that became the foundation of what is now the Thai forest tradition today.
In Sri Lanka the revival had a lot to do with the rising sense of anti-colonial sentiment towards the British who controlled Sri Lanka at the time, with Buddhism growing again as a response to Christian missionaries. This Buddhist pushback started when the Monk Migettuwatte Gunananda Thera began putting out pamphlets refuting Christian missionary literature, and this gave way to a series of debates which culminated in the city of Panadura, and it was the Ven. Migettuwatte Gunananda Thera who won the series of debates.
This sparked the Buddhist revival movement and it was at that point the Theosophical society lent support, and meditation became more common as serious study of texts became more common.
As for Burma, I think the meditative side of revival there is largely the result of the Ledi Sayadaw's influence. He was a major scholar (In Burma, scholar monks are usually more influential) who learned meditation from someone (no one really knows who) from the hills in the Sagaing region, and he popularized that style of meditation through his teaching and scholarly writings.