What exactly is a LDNS request destination in GTM?

An LDNS (Local Domain Name Server) defines the origin of a name resolution request (in other words, a DNS query). From a topology load balancing perspective, the characteristics of an LDNS can be used to direct a query from a particular source to a desired destination. Source characteristics include the LDNS' continent, country, ISP, IP subnet, region, state, or geolocation ISP. Based on these characteristics, a topology record can direct the request to a particular resource, including a continent, country, Data Center, ISP, IP subnet, pool of virtual servers, region, state, and geolocation. The goal is to respond to the query with a destination resource that makes the most sense given the query source.

You might try reading K13412: Overview of BIG-IP DNS Topology records (11.x - 14.x) for some more information. Also, you could refer to the Getting Started with BIG-IP DNS free training.