A "standard" is a level that you decide that something should be equal to or greater than. For example, if you expect your children to get a "B" grade or better in their classes, that's a "standard" that you have for them. You describe standards as being "high" or "low":

I love how their standards for quality are so high.

He's always had low standards when it comes to the opposite sex. I mean, that guy will sleep with anybody.

To "set" a standard for something means to decide what the standard is going to be:

As team leader, it's your job to set a standard for the entire group.

As team leader, it's your job to set a standard so

Setting a standard is similar to "setting" the rules for something:

I'm sorry. I don't set the rules; I just enforce them.