This number defines how many teams will be involved in each match of the tournament. In a 1vs1 type tournament, each person
is considered to be a member of his own team. Therefore, each team only has one member. So, in a tournament that is going to be
1vs1 type format, the "Teams Competing per Match" is 2. This is going to be your standard format and is therefore the default for this field.
If you are still unsure what exactly this field means, just leave the number at 2.
Another way to explain this field is using the name, Free-For-All (FFA). A tournament
having the 1vs1vs1vs1 type format, such as a game of hearts, has 4 "Teams Competing per Match" (aka 4 person FFA). This type of format is also
popular in games such as Risk, where there might be 3 players
all competing against each other. In this case, the "Teams Competing per Match" is 3, since as noted above, each player is considered a team.
In other games such as Starcraft, it's also possible to have 4 teams
of 2 players each. Therefore, you can set the "Number of players per team" field to 2, and set this field to 4, giving you a 4 team FFA type match, with each
team having 2 players.
If you are still not quite sure what this field means, just leave the values at their default settings.