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). The defensive and attacking ratings can be compared according to spatial logic, so his Left Attack strength was pitted against my Right Defence strength and so on.
Rating as a Measure of Overall Team Strength
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, comparing stars is a slightly inefficient and possibly deceiving way of recording team strength. Thus, intrepid Hattrickers have found other ways to compare overall team ratings. Some of the more popular options are Alltid Hattrick, HatStats, LoddarStats and VnukStats.
Its always worth remembering that an overall rating which is higher than your opponents does not mean that you will win the match.