Future is to speak about things that are going to happen. The equivalent in english would be "will". For example: Yo jugaré - I will play. Yo comeré - I will eat.
Conditional is to speak about things that can happen, but they depend on other things. In english it's "would". For example: Yo jugaría si el día estuviera soleado- I would play if the day was sunny. As you can see, most of the time it goes with a "si - if", That's why it's called conditional.
Hope it's clear.