Mars' surface gravity is 3.711 meters / second^2, or about 38% of Earth's gravity.
There is no medical evidence for the effects on Mars' gravity on Earth life. Although we could simulate Mars' gravity on the International Space Station using a centrifuge, (with some mice in a cage for example), this experiment has never been done. Plants have been grown successfully in zero gee, so it is likely they would also be viable in 38% gee.
Long term medical effects of 38% gravity
As of 2022, no studies have researched this question. Once we have real data, please update this section.
Short term medical effects of 38% gravity
People with bad knee and hip joints may find Martian gravity to be a boon. In the far future, Mars might be seen as an attractive retirement location for that reason. (Tho Luna with 1/6 of Earth's gravity may be even more attractive.)
Martian gravity in fiction
Increasing Gravity Inside Long Term Mars Habitations
There is a simple way to increase gravity within a major base on Mars... A centrifuge.
The formula for centripetal force is:
a = r(2 PI / T)^2. (a = acceleration, T = Time to rotate once, r = radius.)
So let's say we make an underground hyper loop railway on a circular track on an angle facing inwards (so when it is at speed, the gravity of the railcar plus Mars' gravity faces directly down to the floor of the car).
If this circular track was 500 meters in diameter, then the car would have to go around the loop every 57 seconds, (say one RPM to round off). The hyper loop railway would have to go 55 meters per second, or 198 km/hour.
The main reason to make it a hyper-loop is to avoid friction from the Martian dust. This speed is doable with Earth trains using today's tech, which have to fight thru Earth's air pressure. (Japan's bullet trains go 320 km/h for example.)
Assuming the train is 100% as long as the track, and that it is two meters wide, then there is 0.684 square kilometres of area for people to exercise or sleep in. If we make the train 3 stories high, then this area triples.
If we find that there are no long term ill effects at, say, 0.8 gees of gravity, the speed of the train could be lowered. Alternately the radius could be increased (giving us more living area), without increasing the speed.
IF, and only if, we find that low gravity is a problem, then people could work 8 hours a day in the low gravity factories or farms. Then live and sleep in an underground habit at Earth gravity. This would also reduce the radiation dose.
Eureka Settlement Proposal:
A rotating settlement habitat is proposed here. The Eureka space Settlement was proposed for the 2019 Mars society design contest.