A block fills the same role as a defense roll.
In other words: if attack value less then either defense or block, the attack misses.
If attack value is greater than both, then it's a hit, with stress equal to: attack roll plus weapon rating, minus (greater of defense roll or block) minus armor.
So, let's suppose you've got a four shift defensive item available (that's block 4 or armor 2), and further suppose that your defense roll in this case wound up as +3. (And further supposing that you have no other source of blocks or armor.)
If someone attacking you gets:
+2 or less: they miss.
+3: if you activate that defensive item as a block, they miss. Otherwise, they hit, inflicting a stress value equal to the weapon rating of whatever they're using (minus two if you activate your defensive item as armor). (Note that this means that someone using a weapon zero attack connects - but does not inflict stress. And you'd get similar results from up to weapon two attacks if you use your defensive item as armor.)
+4 or higher: they hit, inflicting stress equal to weapon rating plus attack total minus three for your defense. That goes to minus four if you activate your defensive item as a block, since that replaces your defense roll. Or it goes to minus five if you activate your defensive item as armor.
Let's consider a second, alternative scenario: As above, except that base defense roll you got came out as a -1.
If your attacker gets:
-2 or less: they miss.
-1 to +3: If you activate your defensive item as a block, they miss. Otherwise, they hit, inflicting stress equal to weapon rating plus attack total plus one (for your defense of minus one). You can, of course, also activate your defensive item as armor, reducing the stress from that hit by two.
+4 or higher: They hit, inflicting stress equal to weapon rating plus attack total, either plus one (if you don't use your defensive item), or minus one (if you use your defensive item as armor), or minus four (if you do use that defensive item as a block).
Does this make sense now?