mathsgiup nailed it.. The statement is meant in the combinatorial sense.
As to what Chris L said, you are absolutely correct about the astrophysical aspects of the "size" of the universe, (except for the expansion part, because the expansion of the universe, as it is currently understood and as it was first suggested, means the increase in the spacetime separation of faraway galaxys from the center of the universe where the Big Bang is supposed to have occured, it does NOT mean that the amount of matter/energy in the universe is changing...).
However, had the initial statement been formulated more accurately, meaning: "The number of POSSIBLE connections in the brain is higher than the upper bound of the number of atoms of CONVENTIONAL MATTER (i.e. in the form of one of the currently known elements) in the KNOWN universe, as of 07/31/2012". With "KNOWN universe" being the key words here, in addition to the combinatorial calculations which clearly yield much higher numbers than 10^88 or 10^100 or even 10^1000, the statement, when stated in the manner above, becomes absolutely CORRECT!!!!
BAM! the answer to end all speculation. You're welcome.
One more thing I forgot to add:
What lead me to believe the statement is meant in the combinatorial sense are the two key words "POSSIBLE CONNECTIONS"
One more thing, great answer shelby, only you are answering the wrong question. "Possible connections" are different from "physical connections" as synapses can detach and reattach to different synapses, hence the word "possible". So, yes at any one time, the max number of synapse connections is in the range you have stated. However, if you check the same brain again, while the number of synapse connections will not exceed the range you mentioned, synapses will be connected differently. Hence, the number of combinations which CAN happen (i.e. are possible) are much higher than the number you stated, and are obtained through combinational calculations.
Hmmm. After reading jdah4's reply, while the statement remains abstractly correct, it is logically flawed since it compares possibilities to actualities...
So I guess it all depends on each person's definition of correctness.
To me, I find that many axioms of science (especially the natural sciences) can be easily deconstructed to seem "logically" wrong. However, most modern scientists care much more about the abstract correctness of a statement than it's logical value... They care more about the actual consequences of a statement than if it makes logical sense...
Therefore, I still believe the statement should be deemed correct...
I have replied so many times, only because I care for accuracy.