Definition
This idiom suggests that a pair of people are enjoying each other's company, and the addition of a third person would disrupt their comfortable dynamic.
They were having a romantic time in the park, but the atmosphere changed when their friend joined, truly 'two's company, three's a crowd'.
We were enjoying a quiet dinner, but the whole evening became a bit awkward when my roommate's friend came over; it was definitely a case of 'two's company, three's a crowd'.
When John and Mary were talking in the kitchen, I tried to join in, but it felt like 'two's company, three's a crowd,' so I quickly left.