I used to use it a lot to improve microwave shielding. The skin depth for microwaves is about a micron, and about 30 MHz it is 10 microns, so aluminium foil is thick enough.
it offers a small amount of shielding. Copper foil is better. The one from 3M shielding tape offers a good shielding suitable for various frequencies from 30Mhz up to 1Ghz
In Radio frequency EMC tests under Equipment/Devices, when the behaviour of the device is not quite well because the equipment is not quite good designed regarding EMC issues, the Aluminium foil tape can be used to obtain improved behaviour. I mean, if some part of a cable is not properly shielded, this can be a weak point of the installation. Therefore, in order to check if the behaviour is improved during the test campaign, the Aluminiun tape foil is used to check it. This measure can improve the results of the tests.
Copper foil could have higher shielding effectiveness due to its higher conductivity but for shielding magnetic fields at lower frequencies (lightning), aluminium foil may be a better choice due to its higher relative permeability (around 2.2).
One of the reasons is that there is no reasonable way to connect indiviual Al tape segments (due to the intrinsic formation of Al2O3 at the surface). Cu tape has no such issue and is often sold with a conducting adhesive to ease application.
Aluminium has "no" magnetic properties .i.e. no additional benefit for shielding low frequency fields like with mu metal tape or iron tape.
The big common problem of all those shielding foil is the contact resistance even when those foils have some kind of conductive glue. Depending on the orientation of the electric field wrt surface of the foil the shielding can be very good (if the E-field is parallel to the sruface)even when the the thickness of the foil is much smaller than the skin depth. By reciprocity the shielding (attenuation) from inside to outside and vice versa is equal.