A counter pick is a champion whose kit starts the lane ahead of the one it faces, before either player does anything clever. It is not a guaranteed win, it is a head start: better trades, safer farming, and more room for error in the first ten minutes.
For a fast feel: search the champion you are about to face and read the left column. Those are the picks that hold the advantage. If you are the one being countered and cannot swap, coaching is the faster fix, because the lane is playable once you know how to trade in it.
A safer laning phase
The favoured side farms with less risk and takes less chip damage, which is what lets it reach its first item on time instead of behind.
Control of the trade timer
The counter decides when fights happen. That is worth more than raw damage, because it means every trade starts on terms you chose.
Pressure the map can use
A lane that is ahead can leave it. Roams, plates and objective help all start with not being stuck under your own tower.
Nothing after twenty minutes
Most laning advantages decay once teamfights start. A counter pick wins you a phase of the game, not the game, which is why converting the lead matters more than the pick.
The summary higher up this page names them; this is where each one becomes something you can check in champion select. The second column is the part people get wrong, because every one of these has a condition attached.
Where one of these clearly decides a matchup, the tool prints it next to the champion. Where nothing clean applies, it shows the name alone rather than inventing a mechanic.