A multi-valued attribute is one that has several values... at the same time. It's not several values joined together into one value, but several distinct values that are grouped together - the techies would call it an array. An example might be if instead of having different fields for home, work and mobile telephone number, there was one field called telephone numbers that contained any and all phone numbers for that person.
The most common multi-valued attribute that is likely to come up is the 'memberOf' attribute from Active directory (or Azure) which contains security and distribution groups.
Where this becomes important is that when a rule looks at a multi-valued attribute, then all of the values are treated as discrete when evaluated for match conditions and if any of the values meet the condition the rule returns 'true' and does the thing. This is great if you're doing a positive match (e.g. 'contains') because in general if any of the values match you want the rule to apply, however you need to be very careful with negative matches (e.g. 'does not contain') because if any of the values meet that condition then the rule also returns a match - e.g. if your rule is 'does not contain: Staff' and the attribute has three values of ['Full Time Staff', 'Physics Staff', 'Cat appreciation society'], it will return 'true' since one of the values does not contain Staff.
This is one of those computer logic things that isn't obvious at first, but makes sense when you think it through and, once understood, opens many possibilities. In purely practical terms though is is often best to stick with the positive matches such as 'contains' or 'matches' when you're working with multi-valued attributes.