Well, to begin with, it's "portentious," not "pretentious." Casca states that he thinks that the miracles and natural prodigies that he has just narrated are portents of something awful happening in the near future.
Let's look at the line (Act I, scene 3) in more context:
When these prodigies
Do so conjointly meet, let not men say
‘These are their reasons, they are natural;’
For, I believe, they are portentous things
Unto the climate that they point upon.
Many ancient cultures held that the universe was an organic whole, and that each part influenced all the others. Thus, Casca fears that the universal order is disordered by some irregularity in just the way a sick body is disordered, and is showing symptoms of its disorder in the manner a person may show symptoms of a disease in many areas not immediately connected with the diseased organ. Since Caesar is a great man, the disturbance to the natural order is correspondingly great. In Act II, scene 2, Calpurnia, Caesar's wife, interprets the prodigies the same way, as a sign that her husband is in danger of murder:
When beggars die there are no comets seen;
The heavens themselves blaze forth the death of princes.
It is a sentiment expressed in other Shakespeare plays; for instance, in Act II, scene 4 of Richard II:
’Tis thought the king is dead: we will not stay.
The bay-trees in our country are all wither’d
And meteors fright the fixed stars of heaven...