If dreams are subconscious activity, how can we remember them at times?

Dreams are stored in short term memory and occur in REM sleep, which is only 1 stage of sleep. Where you wake up in your sleep cycle affects how well you remember dreams. If you wake up directly from REM the dreams will be clearer, if you wake up in a nonREM stage, it can be as much as an hour after your last dream and you likely won't recall it.