We have two computers in our office. We have one internet connection. Can we share the connecting using a hub or we need to have a router?

(Also if I need to have a router, why so?)

it depends if your modem have the function of router or not.
If not, you will need a router else you just need a hub.

the router will give an IP address to each computer you have and then permit the connection to the net...

Guess you refer to a switch if you speak about a "hub". As outlined by aquafolie, as long as your modem acts like a router and provides IP services to your computers, you don't need a router.

But personally I would go with one, since most routers are also able to act as a firewall and intrusion prevention system (while some modems with basic "routing" features do not).