The R number is made up from three things:
a) how long an infected person is infectious for (and whether infectious before symptoms start - ie whether they can be wandering round infecting people before they know they've even got it - something which can happen for about 48 hours with covid)
b) the secondary attack rate - how many of the people an infectious person comes into contact with who will catch it (might be higher with omicron)
c) how many people the infectious person comes into contact with, especially in circumstances favourable for transmission.
The first two are characteristics of the virus/variant itself, and we can do sod all about that. The third is the one that can be changed, and it's why measures are all based on reducing the number of people you come into contact with (limiting non-essential activities and distancing) preventing infectious and likely-to-be-infectious people from coming into contact with others at all (quarantine and isolation) and making the circumstances of contact which does occur less favourable (masks, ventilation)
It is quite likely that omicron has a much higher secondary attack rate than earlier variants, thus increasing the R number.
Plus it seems to evade previous immunity rather better, so more people are vulnerable (as the proportion of the population is immune, the effective R drops, because the secondary attack rate goes down as not all contacts will be susceptible, if immunity can be evaded then it goes back up a bit)