Assuming the shields are of equivalent level:

• Large shields have the highest block value, but are incapable of parrying.
  
• Round shields have moderate block value and a parry multiplier of 1.5x.
  
• Small shields have the lowest block value, but a parry multiplier of 2.5x.

When you parry, your block value is multiplied by the parry multiplier. Due to the parry bonus, small shields can provide the strongest block values. This, combined with the staggering effect, makes small shields the best shields if one knows how to parry properly.

The meter that pops up when blocking is your stagger meter. Blocking damage fills up a stagger bar. If you block too much damage, you can be overwhelmed, which will cause the block to fail and stagger you for a moment. This stagger meter can be increased by eating food that increases your health.

Bonus info: Blocking costs 10 stamina. Parrying costs 20 stamina. Since bosses can't be staggered, using a large shield on them might be best for a strong block to conserve stamina.