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For a couple of weeks Eth 2.0 testnet Medalla hasn't reached finality. What does it mean? What are the consecuenses?

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A super majority of >66% has to find consensus about the canonical chain head. If this does not happen between two or more subsequent epochs, the beacon chain is not finalized.

The consequence is that the beacon chain switches into a quadratic leak state. Basically, nobody earns money by staking anymore until finality is regained. At best, the balance of an optimally performing validator stays neutral during periods of non-finality. (An exception are block proposer awards, but they are rare.)
Offline validators or those disturbing consensus by slow propagation of attestations or aggregations are continuously penalized by initially small amounts quadratically increasing over time.

This continues until a super majority of >66% reaches consensus again by either

  1. fixing the underlying problem or
  2. misbehaving validators dropping off because the penalties lowered their balances below 16 ETH (the minimal staking amount).

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