It's a three-phase motor that can't simply be wired to run on single-phase mains. But don't panic – there's a choice of magic boxes available to do the conversion, each with pros and cons.
Static Converters use capacitors to fake 3-phase, not accurately, but good enough for most purposes. They're not suitable for machines taking a heavy start-up current like a compressor, but probably OK for a mill, drill or lathe.
Rotary converters use an idler motor to balance the phases, and are a good solution for most machines. Their disadvantages are size (big box), noise, cost (due to the extra motor), and low efficiency. (Efficiency is unlikely to matter unless the machine is run a lot. No-one cares about an extra 25% on a small electricity bill, but 25% on a big one will make your eyes water!)
Electronic 'Variable Frequency Drives' have many advantages such as moderate cost, high efficiency, speed-control, soft-start, and other bells and whistles. They're the preferred choice today unless disqualified by one of their disadvantages! They're components that need to be mounted in a simple box. VFDs are sophisticated tuneable devices with hundreds of parameters; it pays I think to buy new and simple because they come with sensible defaults, in contrast to the older industrial models with inch thick manuals intended for trained installers. Most VFDs can only power one motor; they can't be shared, and their output mustn't be switched. Fitting one to a simple machine is usually straight forward but a complicated lathe with a 3-phase main motor and a 3-phase suds pump with contactor switching phases means a fair bit of rewiring. Not impossible, but not plug and play.
It might be worth getting a quote to have 3-phase installed. Unfortunately prices vary wildly and are often shockingly high. Cost seems to depend on how much physical work is needed to make the connection. Are they simply running a wire from a nearby pole, or will they have to dig a trench along the street, with temporary traffic lights and then mending the tarmac? Complications like crossing a neighbours property push the price up too.
As can be seen much depends on the machine, perhaps machines. It's why DC31k asks for more details.
Dave