After each match you will be able to see both teams' match ratings on the right side of the full commentary text. It may look something like this:
EXAMPLE TEAMNAME F.C.
Player rating and team formation (click on this to link to 'evil' stars/line up)
Team Attitude: Normal (or PIC or MOTS -LINK)
Tactic: Attack in the Middle
Tactic skill: solid
Midfield: weak (high)
Right Defence: passable (very low)
Central Defence: inadequate (low)
Left Defence: weak (high)
Right Attack: weak (low)
Central Attack: solid (very low)
Left Attack: wretched (very high)
This gives you an indication of how strong or weak any of the 7 areas of your team play were in the match. If your midfield was stronger than his (e.g "passable" compared to his "weak") then you will have had more possession of the ball in the game and thus more chances to score (this is complicated slightly if he played counter-attacks LINK). It seems that it is a very rare game in which a team with less than 80% possession wins regardless of other ratings, good midfield counts for a lot.
The defensive and attacking ratings can be compared according to spatial logic, so his left attack strength was pitted against my right defensive strength and so on.
Do not think that defense and attack ratings are like for like. It is generally considered that you would need an attack rating around twice or just below twice the quoted strength of his opposing defense rating if you hope to make break-throughs in that particular area of the field. For example: If his central defense is around "weak" I may need a central attacking rating of more than "passable" to be fairly confident of a break-through there. Nothing is certain, though, because of our old friend Random. Even great attack superiority may not guarentee you goals if you had low possession (midfield) ratings
Hattrick by default doesn't provide a way to easily express overall strength of a team, in order to compare two teams or assess the progress of a team. The most primitive measure would be a total number of stars players gained after playing a match. However, due to several reasons, this is a slightly inefficient and deceiving way of recording team strength.
Due to this, it was necessary to find other ways to compare overall team ratings. The most popular option is HatStats.