There is a great explanation here (link also provided below), which I will quote and annotate here for discussion:
Do you have white water marks?
During rain events water may be pushed up by hydrostatic pressure in the ground under the house. This is pressure that builds up under the house from the weight of the water in the soil around the house.
Generally speaking you don't what to install tile over a concrete slab that has a hydrostatic water problem unless it is remediated first.Hydrostatic water pressure is when water from a source higher than the slab is subjecting the slab to water pressure that results in water literally migrating to the surface of the concrete slab. e.g. being next to a mountain side and the slope of the yard adjacent to the house is sloped towards the house.
Remediate the water ingress first, if this is your situation. High moisture within the concrete is not the same as water ingress through cracks or through the concrete directly.
If you have a hydrostatic condition then you need to install perimeter french drains around your house to redirect the water away from the house.
Adherence of thinset
The moisture of the existing concrete floor determines whether the thinset will adhere to it properly, with full strength.
Assuming you don't have a hydrostatic condition, you can test the concrete slab for its moisture content per ASTM C2170 Relative Humidity (RH) test. If you have 80% or less RH then you should be able to adhere to the slab.
Aesthetics of white mineral deposits
As water travels through the soil and up through the concrete it brings minerals with it, that are deposited in the tiles' grout as the water evaporates. This may become an aesthetic concern. You can determine whether this applies to your floor by examining the existing concrete slab for these white deposits.
Membrane or underlayment?
Do not use an underlayment or membrane as your primary mitigation against a hydrostatic condition, but it is generally fine against high basement humidity.
An underlayment will mechanically de-couple the tile floor from the concrete. This would be required if the concrete floor is unstable and cracked or cracking.
For this you will need a rigid membrane that is rated for direct tiling (thinset on membrane). A soft vapour barrier membrane will require a subfloor over top, which gets expensive and laborious. This is can be opted for if you are tiling over a rough and uneven concrete slab, and you wish to add floor insulation.
For smaller cracks there also exist more flexible thinset formulas which you can use locally in the cracked areas.
You can also apply a waterproof membrane over the slab to keep moisture from migrate up through the grout joints that can develop efflorescence (white mineral precipitate).
Keep in mind that you might have intermittent high moisture conditions. If your concrete slab doesn't have a vapor retarder under the slab that comes up the side of the slab to keep moisture from migrating laterally through the concrete slab, then during rain events or when you water the landscaping you might get purges of high moisture migration that goes beyond what is allowable.
If the RH is over 80% then you have to use an epoxy coated system with a cementitious self-leveling underlayment to seal the concrete. Then install the tile over it.