Banias is the codename for the first Pentium M processor. It was introduced in March 2003 and ran next to the Pentium 4-M line. The Pentium 4-M was based on the desktop architecture (Netburst Pentium 4) but equipped with power-saving technologies and lower clockfrequencies whereas the Pentium M had it's own (P6), and more efficient, architecture.
Intel also formed the Intel Mobile Centrino platform with the launch of the Pentium M. A Centrino-laptop consists of a Pentium M, an Intel i855 chipset and an Intel 2100 or 2200 WiFi adapter. An often seen misconception is that people think that their laptop had a Centrino-processor which of course doesn't exist as it's just a name for the platform.
The successor of Banias is the Dothan core.