Shomer (שומר) is a Hebrew word that literally means "to guard." It can be used to describe someone's occupation (e.g. He is a museum guard) or to describe an action (e.g. He is guarding the museum entrance).
Shomer is also a Halachic term used to describe a person who is "guarding" a tradition by practicing it to the letter. For instance, if a person keeps kosher (meaning they follow Judaism's dietary laws of kashrut) they can be described as "shomer kashrut" because they are guarding the laws of kashrut. Likewise, someone who is "shomer shabbat" observes all the laws of shabbat. In a sentence this usage of shomer could look like this: He is shomer kashrut, so he doesn't mix dairy and meat. (The laws of kashrut forbid mixing milk and meat.)