What is boost supposed to mean?

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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?
 
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To change its velocity.
 
then what does it have to do with momentum (generator of spatial translations)?
 
ChrisVer said:
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:

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