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
Tactic skill: (no tactic)
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). It seems that it is a very rare game in which a team with less than 20% possession wins regardless of other ratings; good midfield counts for a lot.
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.
Its always worth remembering that an overall rating which is higher than your opponents does not guarantee a win. Individual ratings are more important although the overall rating is nice to know.