To be caught with your pants down means to be caught unawares in a situation to which you are completely unable to respond, react, etc. This expression means much the same as being a “deer in the headlights” except that the situation of the person caught with their pants down is highly embarrassing or potentially damaging, etc. This often involves a sexually compromising situation or something else one should not be doing. As well, it can simply mean that someone is unprepared to act and this lack of preparation is bad for their reputation, career, etc.
The idiom is similar to caught red-handed except that it does not involve being caught committing a crime. It is also similar to caught with your hand in the cookie jar.