What is the setting and hardening of cement?

Setting of cement is the initial solidifying of the cement.

I presume you will not be using a cement material by itself, but by mixing in aggregates and fines to create 'concrete' I will continue this answer talking about concrete but much still applied to a simple cement mortar also.

Depending on temperature (warm fast, cold slow) initial set will be between 2 and 24 hours. This will result in a concrete material that can easily be marked with a fingernail.

Once the concrete has set, the concrete goes through a process called curing or 'hardening' where the pozzolanic constituents of the concrete 'hydrate' (react with the water) to create a hard material. This will continue for the life of the concrete but the most significant strength gains will be noticed within the first 28 days and this is the strength normally taken as the design strength of the concrete.

It can be expected in ideal conditions with warm air and a light breeze in the air, for the concrete to achieve

30% of it's 28 day strength in 1 day

60-80% in 3 days

80-100% in 7 days

and 100-% in 28 days

Many factors will affect this.

temperature will have a large impact.

additives such as retarders and accelerators can be added to slow and speed up the hardening process respectively.