What are the types of lookup caches?What is Dynamic lookup Transformation? when we use?

Static, Dynamic, Persistent, Re-cache. 

Dynamic lookup updates cache before writes data into the target, first it will update cache then only it updates target table. Generally we are using it in SCD's. 

Dynamic Lookup are used for implementing Slowly Changing dimensions. The ability to provide dynamic caching gives Informatica a definitive edge over other vendor products. In a Dynamic Lookup, every time a new record is found (based on the lookup condition) the Lookup Cache is appended with that record. It can also update existing records in the cache with the incoming values.