Assets (table: asset) are things that are quoted in the market and traded. An example of an asset would be the equity APPL, or the currency USD.
Rates (table: rate) are a class of prices or rates that are quoted against an asset. For example, a 2 month GBP/USD spot rate is a rate that is quoted on the exchange of GBP assets for USD assets (which itself could be thought of as a single FX asset) for settlement in 2 business days.
A Rate Value (table: rate_value) is a particular instance of a rate - often an observation of the price of an asset at a particular time. For example; the GBP/USD rate on 2009-11-11 at 15:15 GMT was 1.6654. You might want to store perturbed rate values for use in scenario analysis.
Rate Groups (table: rate_group) are a universe of rate values for different rates that you want to group together, typically so you can use them for pricing. For example; you may have a rate group labelled "2009-11-11 CLOSING", that contains the rate values you want to use as the official close-of-business rates.
A Rate Series (table: rate_series) is a collection of rate values for the same rate.
Term Structures (table: termstruct) are yield curves, forward curves, or volatility surfaces that you build in order to facilitate pricing. You define a term structure in the DOPE by listing the rates that you would use for building that term structure. For example - A USD yield curve may be constructed from USD bill rates out to 6 months, then Bill Futures out to a year, and then swap rates going past that.