If you're immodest, you tend to brag about your abilities — you're not at all humble. It would be immodest to boast about your experience making movies, especially if all you've actually done is take videos of your dog in the back yard.
There are two ways to be immodest: the first is to gloat and show off, essentially being the very opposite of modest. The other way is to lack good taste and restraint. Years ago, it would have been considered immodest to wear a bikini to the beach — while today, it's only immodest if you wear one to school or a restaurant. The "arrogant" meaning came before the "improper" one, both from the Latin modestia, "moderation," and "correctness of conduct."