This may sound obvious, but how can you tell how much health your units have in Civilization V?
There's several ways to determine a unit's hit points:
In the lower left hand side of the screen, you'll see an info panel with a small bar on the right side. If you hover over this bar, you'll see the unit's current hit points.
When looking at an area on the map, only damaged units will show a bar with their current hit points. You can see the musketman garrisoned in Onondaga and the cannon southwest of it are both damaged, and they both have hit point indicators to the right of their unit symbols.
Hit points on almost all units are measured on a scale of 10, but unit strength, alongside defense and attack modifiers, limit how much damage they deal and receive from other units.
Cities also have hit points, which you can gauge by the bar above the name of the city. In this case, directly above the word Onondaga you can see that that city has recently taken damage which it has not yet recovered from. City hit points are measured differently, and you can gauge a city's relative strength by the number next to the shield on top of the name.