sql server cache clock hands
Correct me if I'm wrong but as I understand it is that SQL Server uses a CLOCK algorithm for the cache- and userstores. Each clock has two hands, an external and an internal.


Yep, almost like what you have said but let me add something more. Cache and Userstores shares common costing and algorithm called as Least Recently Used(LRU) algorithm. This LRU mechanism has what is called as "clock algorithm". This algorithm has what is called as "hands". There are various eviction policies which work inside SQl Server to remove "old" entries from SQL Server caches and to help this SQL Server has 2 clock hands:


External: Implements Global policy
Internal: Implements local policy


Policy is something which you can consider as rule when dealing with removing old entries from caches.


  If a worker that accesses a cache notices that a cache is greater than a certain percentage of memory, the internal clock hand starts to free memory for that cache.


There is lot more that happens it is not like that internal clock will "only" free memory by removing old entries after total memory utilized is  greater than certain percentage, LRU and internal memory pressure is also taken into the account. 


  What is the difference between last_tick_time and round_start_time? Is the cache not cleaned when the hand is moved?


last_tick_time - time when a clock hand moved last.

round_start_time - time when a clock hand started current round. The round which it did to sweep the caches.


  How many entries get removed with each tick of the clock?


There is no predefined value, after LRU algorithm has done its task other thread would see how many entries in cache are "old" and then would remove it. If there is memory pressure the value may increase and the sweeping may happen too often.


  Can somebody helps me understanding the working of this clock algorithm in SQL Server


Slava Oaks from Microsoft has already written a lot about it. I will quote from his blog


  In SQL Server 2005 we introduced new common caching frameworkAll caches except for Buffer Pool leverage it. The framework consist
  of set of stores and ResourceMonitor. There are three types of stores:
  cache store, user store  (the name here is related to internal usage
  of the store - it does not have to do anything with a user)  and
  object store. Both cache and user stores share common LRU mechanism
  and leverage common costing. Procedure cache is an example of a cache
  store and metadata cache is an example of a user store. Object stores
  are just pools of memory blocks and don't require either LRU nor
  costing. Network library leverage object store for pooling network
  buffers.
  
  Store's LRU mechanism is a rather simple - we use variation of
  thoroughly discussed in operating system's literature clock algorithm.
  As you remember clock algorithm has a hand. When hand moves it
  decreases a cost of an entry. Once cost of an entry reaches 0, the
  entry can be discarded from the cache. Cost gets reset whenever an
  entry is reused. When dealing with multiple caches a designer has to
  take into account global and local eviction policies. Global policies
  consider global picture and enable running of LRU, clock algorithm,
  across all the caches. In its turn, local policies look at the local
  resource consumption only and run LRU for a given cache only.
  
  In order to satisfy global and local policies SQL Server's stores
  implement two hands: external and internal (please don't confuse a
  clock hand names with types  of memory pressure. There is no
  connection!). External clock hand implements global policy and
  internal clock hand implements local policy. Even though every cache
  has its own external hand, external hands move "synchronously" - one
  at a time. Their task is to simulate global hand.


Additional Reading: The Clock Hands of Buffer cache