Remember is the opposite of forget, and in many cases it is involuntary - you remember some things, you forget others. Memorise (or memorize in US spelling) is the conscious process of committing something complicated to memory. You might sit down at your desk and memorise a list of dates for a history exam, or the details of different chemical elements for a science exam. You could memorise poetry, in the sense of learning every word by heart. 'remember' can also be a conscious act, but it's usually for something much simpler, such as 'I must remember to post that letter.'