Workers can repair without spending a charge.
The biggest change in 6 was the expulsion of many city improvement buildings and wonders to tiles outside of the city center. Now every wonder must be built outside of he city center with some sort of terrain requirement (I.e., the Lighthouse of Alexandria must be built on a coast tile adjacent to a harbor, a new district). The majority of city improvements now belong in respective districts that provide yields on their own, with varying strength depending on their adjacencies. Civ 6 is very interested in a tile adjacency game that has not really existed in previous installations.
Combat is in 6 is resolved by difference in absolute rather than relative strength difference (as in 5) (which sounds small, but really makes keeping up with the most advanced units much more important). In the late game, similar units can be combined into stronger one tile units called corps, armies, fleets, and armadas. There are also fewer units in an upgrade line in 6, with about one upgrade every other era.
Social policies are now swappable powers that go into slots that belong to your government type, rather than permanent commitments. You are never locked down to a social policy for the rest of the game in 6, but you may only have fewer active at a given turn)
Many technologies that belonged to the common science based tech tree in previous games were moved to a separate culture based civics tree, giving culture focused civs a chance to advance without needing to hard into science. These upgrade government and social policies faster.
Civ 6 does not feature a diplomatic victory seen in previous games. City state (minor civs introduced in 5) relationships are governed by investing a new currency of envoys into each city state, earned in a few different ways, but never through gold. Each city state has a unique bonus granted to the lead investor. Additionally, city states provide an increasing yield to the player based on number of envoys sent regardless of whether or not they are the city state’s ally and lead investor.
And there’s a religion victory now.
There’s some other small changes, but these are probably the most important differences.