Desdemona is young and has been living a very sheltered life.
"She loved me for the dangers I had passed/ And I loved her that she did pity them." .
It is also very clear that they have not been married with Brabantio's blessing, and that Othello has only 'got away' with this secret marriage as he is so highly respected, treasured and needed by the army. This also shows us of his privileged position in society even though he is black - basic background knowledge which we need. Brabantio's warming to Othello also weakens our opinion of their chances of happiness.
"Look to her, Moor, if thou hast eyes to see:/ She has deceived her father and may thee." .
Without all this information we would be ignorant of the weak basis of the marriage, and therefore confused by how easily Iago manages to ruin it so completely later in the play.
The last thing that Act 1 really shows us which effects our understanding of the rest of the play is Iago's plans of apparent 'revenge'. His soliloquy in Scene 3 is a massively important turning point in the play, where it all starts to go horribly wrong for everyone but Iago. Iago clearly reveals his true self with comments such as 'I hate the Moor' and we hear his deceitful, back-stabbing plans.
" The Moor is of free and open nature/ That thinks men honest that but seem to be so/ And will tenderly be led by th'nose/ As asses are".
Shakespeare has clearly stated to the audience and readers that Iago is intending to use Othello's open nature and trust for him to his own advantage, and to destroy Othello.
"After some time to abuse Othello's ear/ That he [Cassio] is too familiar with his wife./ He hath a person and a smooth dispose/ To be suspected, framed to make women false.".
Here is where it becomes really very clear exactly what Iago is planning, and how well he is planning it. It becomes clear to us that Iago is a very clever but bitter and somewhat twisted man.