What is 1P?
Selling to Amazon Retail via Vendor Central Interface
High volume sales directly to Amazon
Listing priority and optimization on the site
Potential for enhanced credibility as items are being sold and shipped by Amazon
What is 3P?
Selling through Amazon Marketplace directly to consumers via Seller Central Interface
Ability to set prices
Fulfill orders independently or have them fulfilled by Amazon
Have greater control of brand identity
Can I Use 3P if I Already Use 1P?
It is possible to have both channels with Amazon, though generally only items that a vendor does not list through a 1st Party channel may be sold through a 3rd Party channel.
These are the basics, but the decision of whether to utilize a First Party, Third Party, or combination strategy can be a nuanced and complicated one and is worthy of further research.