What is boost supposed to mean?

[ChrisVer]

What does it mean to boost something along the z axis?
To give some acceleration to it, or to spatially translate it? I think it's the 2nd?

 

[Vanadium 50]

To change its velocity.

 

[ChrisVer]

then what does it have to do with momentum (generator of spatial translations)?

 

[Matterwave]

then what does it have to do with momentum (generator of spatial translations)?

Can you be more specific? A boost (or any Lorentz transformation, for that matter) $\Lambda_{~~\nu}^\mu$ changes the momenta of particles in a predictable fashion:

$$p'^\mu =\Lambda_{~~\nu}^\mu p^\nu$$

 

[WannabeNewton]

A boost corresponds to Lorentz transformations that aren't spatial rotations. They correspond to $K_i= J_{0i}$ where $J$ are the Lorentz generators. The momentum of a massive particle defines a preferred boost axis.