Consider these following two structures from the same compound:

The two Newman projections are along the horizontal $\ce{C-C}$ bond which is, of course, freely rotatable. The two structures represent two possible syn-elimination transition states. Note that in the left-hand structure there is a steric clash between the tert-butyl group and the methyl group. The right-hand structure has no such clash. It is therefore the preferred transition state for this reaction.

‘Less hindered hydrogen’ basically means that hydrogen that leads to the more stable transition state.

Consider these following two structures from the same compound:

The two Newman projections are along the horizontal $\ce{C-C}$ bond which is, of course, freely rotatable. The two structures represent two possible syn-elimination transition states. Note that in the left-hand structure there is a steric clash between the tert-butyl group and the methyl group. The right-hand structure has no such clash. It is therefore the preferred transition state for this reaction.

‘Less hindered hydrogen’ basically means that hydrogen that leads to the more stable transition state.