When you 'board' something, you are getting on it. 'Embark' is when that something leaves.

When you use "board" you have to specify what you are boarding, as in "we boarded the ship". With embark, you don't use an object, as in "the passengers prepared to embark." (the ship) You can also use "embark" to say that you embark on a journey or a voyage. (Following with the preposition "on") Hope this helps :D