LCD uses backlights to illuminate pixels while OLED uses Light-Emitting-Diode which enables each pixels to light up themselves. You can view LCD as a subtractive and OLED as additive. Sometimes LCD is called transmissive and OLED emissive. The concept should be easy to understand for most folks.
Burn-in on OLED is caused by uneven wear of the pixels (diodes). It has been known that blue diodes do not have as long a life expectancy as red and green diodes. This is why Samsung uses Pentile matrix for their AMOLED panels and always tweak the shapes of sub-pixels and the distances between them, etc. Presumably they are trying to find the best combination of sub-pixel arrangement to accommodate other technical advances. (e.g. improving brightness and power efficiency)
The pros and cons of OLED (v. LCD) have been debated to death. LCD has generally provided higher peak brightness (although this seems to be changing), is more resistant to burn-ins, and is more power-efficient in today's web environment where white backgrounds dominate. OLED's advantage comes mostly from its lack of backlights, which in theory and practice provides infinite contrast. This means OLED does not need to match LCD's brightness for comparable legibility in a given environment, while its true black offers visual fidelity that cannot be matched by even the most advanced LCD technology. Another advantage of OLED is that it can be "printed" on pretty much any surface because it does not require backlight, and this makes curved display possible for smartphones.
Burn-in is an issue for any display technology, but it is particularly acute for AMOLED due to the way tech works. The question is a matter of degree, and what kind of tolerance level Apple will set for its products. It is about balancing the benefit and cost, then finding the optimal middle ground.