If you wish to visit someone's profile, you just need to find that specific connection and then click on the ellipsis (⋯) - More Menu - on the right-hand side of the connection row and select Visit Profile option.
Upon clicking on Visit Profile option, a new tab will open up with that connection's LinkedIn profile page.
You can also decide to visit multiple profiles by ticking the checkbox on the left-hand side for the connections you wish to visit and then clicking on the Visit Profile button in the action bar.