1:8 What does the word "sober" mean here?

Sober here means be discreet, temperate, to curb one's desires and passions (cp 2:5; 1Ti 3:2, 11).

In Tit 2:2 sober means to be self-controlled, especially in respect to wine (cp Tit 2:2; 1Th 5:6; 1Ti 3:2, 11).

In Tit 2:4 sober means to encourage self-control, self-discipline (cp Tit 2:4).

In Tit 2:6 sober means to be in one's right mind, of sound mind, sane (cp Tit 2:6; Mk 5:15; 2Cor 5:13; 2Ti 1:7).

Sober is also used in scripture metaphorically, meaning vigilant, watchful, circumspect (cp 1Th 5:8; 2Ti 4:5; 1Pe 1:13; 4:7; 5:8).

See also comments on Ro 12:3, 1Pe 4:7-11, 5:8.