I see the linux-hwe-generic package as part of the kernels you can install in Ubuntu 12.04.
What is hardware enablement (HWE)?
Brand new hardware devices are released to the public always more frequently. And we want such hardware to be always working on Ubuntu, even if it has been released after an Ubuntu release. Six months (the time it takes for a new Ubuntu release to be made) is a very long period in the IT field. Hardware Enablement (HWE) is about that: catching up with the newest hardware technologies.
Now, how does Ubuntu want to reach the goal of Hardware Enablement? Using rolling releases for the kernel: as soon as a new kernel is released, it is packaged for Ubuntu, tested (via the proposed pocket and special Q/A methodologies), and made available to Ubuntu users. This method has of course some disadvantages: releasing a new kernel too quickly may introduce some bugs and issues, and may not be suitable for the enterprise.
The solution? Offering different kernels for different users. Therefore Ubuntu will offer at least two kernels: the General Availability (GA) kernel, i.e. the most stable kernel, which does not get updated to point releases; and the Hardware Enablement (HWE) kernel, i.e. the most recent kernel released. This is why you are seeing both the
There is a wiki page that explains some plans about kernel rolling releases and hardware enablement, and also cites the
Finally, if you are interested in developing or testing the newest kernel technologies, look at the Ubuntu Hardware Debugging web site.