to watch
The translation provided is incorrect. 'Veranear' in Spanish does not mean to 'watch' in English, but it refers to spending the summer or the summer vacation period somewhere, usually at a holiday location. It is most commonly used in Spain and parts of Latin America to describe vacationing during the summer season.
I'm going to summer on the coast this year.
In this phrase, 'veranear' is used to express the concept of spending the summer period, usually involving holidays, in a certain place. Here, it's the coast.
I love to summer in the countryside with my family.
Similar to the previous example, here 'veranear' is used to indicate spending the summer period in the countryside. The speaker also adds the quantifier 'con mi familia' to indicate who they're spending the summer period with.
We used to summer in the mountain when we were children.
In this instance, 'veranear' is used in the past ('solíamos') to refer to a recurring summer activity in the speaker's childhood. The activity again is spending the summer in a place, this time in the mountains.