What does attest to the head of the beacon chain mean

Question

I am reading an overview of the beacon chain here and I came across this section I do not understand:

Validators are split into “beacon committees” at each epoch (defined 1 epoch in advance to allow for preparation). Each committee is assigned to a slot (and shard in Phase 1). And each validator in the committee attests to the head of the beacon chain (and the recent data of their assigned shard) at their assigned slot

What does "attest to the head of the beacon chain" mean? Does the head of the beacon chain mean the latest block on the beacon chain? If so what does it mean to attest to it?

Answer 1

Does the head of the beacon chain mean the latest block on the beacon chain?

"The head of the beacon chain" is officially defined as the result of running the get_head function.

The get_head function is too complex to describe exactly here, but it can be loosely understood to run the LMD GHOST algorithm on the block tree and return the head block with the most* votes (attestations) from other validators.

From a stratospheric high-level view, the head of the beacon chain can be found by looking at all the conflicting chains (forks) of the beacon chain and then choosing the chain which has received the most votes from validators. The latest block in that chain will be the head of the beacon chain.

(* LMD GHOST doesn't necessarily select the head with the most votes since it's a "greedy" approximation algorithm).