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Can you explain: table fact, dimensions, and OLAP?

The following is unclear to me, can you explain: table fact, dimensions, and OLAP? Also, regarding EAI vs. DW as an integration solution -- what are the differences between EAI and DW?
OnLine Analytic Processing tradtionally splits a relational view into several dimensions, such as time, product, region, etc. This allows ad hoc drill down and aggregation to be performed in advance of the user query, although the cost in storage space is generally higher than what is required for a relational solution.

As far as EAI vs. DW, the first is the means and the second is the end. EAI is used to aggregate information for a data warehouse.

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