Prospect is a potential customer.

Lead is a business opportunity that can lead to a Sales Order. Leads can be related to customers (repeated business) or to prospects (new business).

Partner is a generic term for an entity (person or organization). Customers, suppliers and prospects are all "partners".

Contact is a person (name & address) related to a Partner. Before v7 Contacts were stored in a separate model (res.partner.address). In v7 Contacts are also stored in the same model as the Partners (res.partner).

To add a little bit:

Prospect is a potential customer, but is not an existing object in OpenERP. For example, a prospect can be an existing partner or not.

Lead/Opportunity: They are sales opportunities. The difference between a lead and an opportunity is that the lead is quite a remote probability. Something like, you heard of a potential need for a prospect. Once you contact the prospect, and it confirms that there is an interest, the lead becomes an opportunity (hence more fields).

You can find a bit of information here (in french though):

http://openerp.cogitae.net/doc-module-crm-vente/

http://www.youtube.com/watch?v=vpJuF8BJ_Ec