Can someone explain what 'vest shares' means and its implication(s)?
In simplest terms, Vests are another name for powered-up Steem, i.e. Steem Power.
In more technical terms, powering up Steem purchases Vests which can be considered as a share of the overall voting rights of the Steem reward pool, hence the term "vesting share."
One interesting point is that the amount of Vests purchased by a Steem Power power-up remains unchanged over time. However the amount of the Steem Power purchased actually increases over time due to interest being added. 15% of the Steem inflation is used to add interest to Steem Power holdings. Thus over time each 100 Steem power-up actually purchases fewer Vests.
When you look at the blockchain transactions, the author rewards and curator rewards are not expressed in Steem Power but in Vests. Your Steem Power holdings are also actually recorded in Vests.
But broadly speaking, Vests are Steem Power.