1. beginning to understand or become aware of something
Usage: informal; often used with ‘on to’
2. beginning to like or take a liking to someone or something
Usage: informal; often used with ‘to’

Examples

• She’s finally cottoning on to the new software system.
• It took him a while, but he’s cottoning to the idea of moving abroad.
• The students are cottoning on to the teacher’s methods.
• I’m cottoning to this new restaurant more each time I visit.
• He’s slowly cottoning on to what really happened that night.
• The team is cottoning to the coach’s strategy.