A fan trap is where, in a data model, you have a m:1:1:m set of relationships; that is a central entity/table has a 1-to-many relationship on each side of it. Because of this set up, it’s not possible in a relational databse to specifically relate an individual record in the entity/table on one side of the set of relationships with a record in the entity/table in the other side. (If you draw out a simple diagram with the 3 entity/tables, you’ll probably see this more clearly.) Hence it needs to be resolved by restructing the data model, if there is a need to generate reports based on these 3 entity/tables.
A chasm trap is a bit more difficult to explain without a diagram. A chasm trap is where you have a 1:m:1:m set of relationships between 3 entity/tables and the relationships are optional (ie there may, or may not be, a record on the ‘1’ side of the relationship for a given record on the ‘m’ side). In this case, if you are trying to link records from the entity/table on one side of the 3 with those on the other side they won’t all connect and any report you construct could give false info. Again, data model redesign is required.
Hope this helps. Any half-decent Database Design book will have these explained, and probably in a far clearer way than I’ve done here!