As a Seventh-day Adventist (we observe the Sabbath by going to church on Saturday -- but that can lead to an entirely another discussion), I personally view it as a time to disconnect from work, and focus on God, relationships, and the nature around us.

In terms of hobbies, this is interesting a point of debate with many Adventists. Some are more 'conservative' where they won't do anything close to resembling work or hobbies (similar to some Orthodox Jews), and you have the other spectrum of people who more liberal in a sense where they will still do their hobbies (like going to movies, playing sports etc).

I think it is a personal thing to each person, but the overarching themes is really taking a day out of the week to disconnect from the trials of the world and spend a day for a mental reset however you choose to accomplish this.