I have a Merida hybrid cycle fitted with Shimano XT Deore 3 x 8 speed (42/32/24T). The crank has a few worn teeth and I would like to replace with Shimano XT Deore (48/36/26T). The seller states this is for 3 x 9 speed gear set, can I fit to my cycle?
Yes, there are no complications with running a 9 speed crankset on an 8 speed drivetrain. You can see image below that some 9 speed cranks are even listed as being 9/8 speed cranks. You shouldn't encounter any problems, but you will have you readjust your front dérailleur to make room for the larger ring, and double check your chain length on big rings after it's installed.
Strictly speaking, one crankset will have been manufactured for an 8-speed chain, the other will have been manufactured for a 9-speed chain. That is basically the difference between the two.
The external widths of an 8-speed chain and a 9-speed chain differ by something like a few tenths of a millimetre. It is arguable whether this amount makes any practical difference to your shifting experience.
On the one hand, the bike companies will say that it does. Everything that is part of the chainset will have been manufactured precisely, based upon a certain chain width, and anything different will give you an "imperfect" experience. But then the bike companies also have a vested interest in selling you components.
On the other hand, the difference is so small that many people happily run this setup without reporting any ill-effects.
Aside from this, I agree entirely with @ShemSeger's answer, but I did think it was important to emphasise to you that there will be a difference, albeit slight, between the two cranksets.
The front is effectively independent of the back - a triple which is "9 speed" should work fine if you replace it with a triple "8 speed" and vice versa (the speeds for the rear when marketing front cranksets are marketing). Similar with derailleurs in the front vs whats going on in the back.
You will probably need a new chain, and you need to see if the front derailleur is even rated to take a 48t (which I suspect it probably isn't). This can be done by checking the spec sheet for the front derailleur. If not, you need a FD which has the same cable pull as your shifters which has the capacity.
Also, on a Deore XT crankset, you can buy replacement chainrings and install them, so you could save a decent amount of money this way.