In my opinion their explanation is both flawed and potentially dangerous.
In electrical terms 'to isolate' means 'to disconnect from'.
An isolating transformer isolates the primary circuit from the secondary circuit.
That means they are electrically insulated from each other. Their only linkage is through their common magnetic coupling.
This is required for safety rather than signal reasons. It limits the effect that a fault condition in the primary (secondary) can have on the secondary (primary). It also means that the maximum current that may be supplied to the secondary circuit can be limited to a safe value as is done in bathroom shaver sockets. This limit is imposed by the magnetic characteristics of the transformer core.
Most transformers are used in this way and are, in fact, isolating transformers. This applies from large megawatt transformers in national power grids, to transformers supplying individual items of equipment in your home or workplace, to sniffer loops connected as inputs to electronic instrument.
Transformers that are not isolating may be simple autotransformers with only one winding. Here the secondary is actually a tap on the primary so there is clearly no possibility of electrical insulation or isolation. Bench variable transformers (variacs) are of this type.
Or the transformer may have two (or more) separate windings, but the designer (constructor) of the equipment has grounded (earthed) one end of both the primary and secondary windings. Since there is now a common electrical connection the isolation is lost.
Isolation (1:1) transformers are smaller, and normally used in PSUs, where any contact with the mains is not desirable. For example, isolation transformers are used in flyback PSUs, since otherwise one of the terminals could be hot if the plug is connected in a certain way.
so tis answers is very good but when I need to use the isolation transformer
I am a new electrical engineer in gas plant and for the extention of the plant we need to install isolation transformer to feed the UPS system and external safety lighting
and I want to know why I used isolation transformer especially for these loads in addition we did not use it for other loads
The galvanic isolation offered by the isolation tranformer makes possible safety levels in the secondary winding power driving. It permeats that any disturbance, like a short circuit, not affect to the main circuit and the operators by the local fuse use. If a short circuit happends the local fuse ( in secondary) burn it and the circuit will be isolated from the main circuit without possibilities of make larger damages.
For that (and others reasons), it is very used in oil and gas factories and rigs.