To snog someone means to kiss and cuddle them in a passionate way.
Snogging is usually seen as something young people do, and it can be seen as romantic or a little bit naughty.
Examples:
They snogged behind the school.
She snogged her boyfriend at the party.
He likes to snog his girlfriend in public.
The dog and the cat snogged in the garden.
In the movie, the prince and princess snogged in the castle.
I saw them snogging in the park yesterday.