What is Loss Assessment Coverage?

You should ask your insurance agent with regards to the specific policy (all the terms are defined in each policy, and may differ). Generally it covers the special assessment HOA imposes when there’s a loss on a common property (what you said).

Here’s a quote from State Farm, check your own insurer for definition applicable to your policy:

Loss Assessment

Coverage D

This valuable condo insurance coverage is uniquely designed for owners
in condominiums/ associations. It recognizes the potential for owners
to be assessed for certain kinds of loss. Here are examples of
circumstances that might require the condominium association to assess
all unit owners:

• Someone is seriously injured on common property (perhaps at a swimming pool) and the courts award a judgment that’s higher than the
  amount of liability coverage provided by the condominium/association
  policy.
• Major damage occurs to commonly owned buildings and it is not fully covered by insurance.

In either case (and other similar cases), loss assessment coverage
would pay your share (up to stated amount). You should review the need
for this coverage with your agent and buy an appropriate amount of
coverage.