A cusp is the moment one sign changes to the next. The cusp between Leo and Virgo happens at a precise moment, which varies from year to year. If you were born before it you would be Leo, and after it you would be Virgo.
The moment of the Leo Virgo cusp is not related to calendar dates. It's not as simple as saying August 22nd is always Leo and August 23rd is always Virgo. One year the cusp may be at 11pm at night on August 22nd, and the next year it may be early in the morning on August 23rd etc.
To find out for sure which sign you are you will need to know when exactly you were born. Specifically you will need to know:
With that information an astrologer can calculate which side of the Leo Virgo cusp you were born on, and therefore which sign you are. For example, this calculation is always performed as part of my natal readings (for one person) and relationship readings (for couples).
If you don't know your birth time then things get a little more complicated, but it is often possible to figure it out "backwards" from major life events. That's a technique called birth time rectification. I won't confuse things here by going into it, other than to say it exists for that scenario.
Another way to establish which sign you are is simply to look at the list of Leo traits compared to Virgo traits. Leo and Virgo have very different characteristics so it's often fairly easy to see which one you are.
In some cases however people relate almost equally to both signs. In that situation it's going to be because your sun sign is one of them, while you have another planet (most often mercury) in the other. For example you may have your sun in Leo and your mercury in Virgo.
In that situation you probably will need an astrologer to tell you which is which, and explain how they interact. There are a large number of permutations so trying to cover them all here would be very confusing, but I automatically include your specific planets and interactions in all my natal readings (for one person) and relationship readings (for couples) mentioned above.
Leo man
Leo woman
Leo compatibility
Leo profile
Leo seduction
Leo in love
Leo relationships
Virgo man
Virgo woman
Virgo compatibility
Virgo profile
Virgo seduction
Virgo in love
Virgo relationships