For example, let's say you have a visibility rule that should display the a particular field when 'Marketo Lead Management' is selected for the "Product Interest" field. The displayed value for the field (the one shown to the customer) may be "Marketo Leads Management" but the stored value for the field (the value written to the lead record) is "MLM".
If you set up the visibility rule as "Product Interest is Marketo Leads Management", the rule will look at the Display Value and see a match. However, "Product Interest contains Marketo Leads Management" will look at the Stored Value, which is "MLM." It will not see the match, and the field will not be displayed.