When we say something travels at 50% the speed of light, it's always relative to some inertial, approximately inertial, reference frame, often implied.

So eg. if you hear about the particles at the LHC travelling at near the speed of light, it's implied that's relative to the Earth.

The speed limit comes in here: no-matter what nearby object you look at, its speed relative to you always be less than the speed of light. (Here, nearby means something like "within the local group of galaxies" - objects a long way away can be receding faster than the speed of light due to the expansion of space in between you and the object). You can accelerate as much as you like for as long as you like and when you stop accelerating and check, that'll still be the case.

"that speed is relative to what"

To you. There is no such thing as absolute speed. You say cosmic rays are crashing into the earth at 99% the speed of light. The cosmic ray says it is sitting still and you (and the Earth) are approaching it at 99% the speed of light. Some other particle moving at 70% relative to you will give a different speed for the cosmic ray. All of you are right.

No matter of fast you are moving, you will agree with a “stationary” observer about the speed of light. What you won’t agree on is the color of the light. Apparent frequency shifts to maintain the speed of light. The color shift is how we know how fast stars are moving relative to us.

Higgs field is present everywhere and mediated by Higgs boson, so just measure speed relative to Higgs field. Or you can measure speed relative to CMB.