I have read the 'The Sims 3 system requirements' but I still dont understand whether a Mac Book would run the Sims 3. This is the information provided on the Apple website;

Mac OS X v10.5 Leopard

NVIDIA GeForce 9400M graphics processor with 256MB of DDR2 SDRAM shared with main memory

2.13GHz Intel Core 2 Duo processor with 3MB on-chip shared L2 cache running 1:1 with processor speed
1066MHz frontside bus
2GB (two 1GB SO-DIMMs) of 800MHz DDR2 SDRAM; two SO-DIMM slots support up to 4GB

160GB 5400-rpm Serial ATA hard disk drive
8x slot-loading SuperDrive

I think the bit that I dont get is the Mac OS X v10.5 Leopard bit as it says on Apple a new version is going to be released - Mac OS X
10.6 Snow Leopard??? I dont know if the older version would work or only the newer version.

The 9400M version would be fine. Older versions with IGPs will either not be ideal or may not work at all, especially if you plan on running in bootcamp.

If you're looking specifically for something to buy to run the Sims games, I suggest not buying a macbook. The price/performance ratio is awful and you can do much better if your intention is to play games. Macs serve their purpose - gaming is not one of them.

I invite you to check out our sticky help threads here. Tons of information.